Professor Igor Shparlinski

Abe M; Aoki K; Ateniese G; Avanzi R; Beerliová Z; Billet O; Biryukov A; Blake I; Boyd C; Brier E; Castiglione A; Cha J; Chan A; Chen L; Cho K; Contini S; D'Arco P; Ding J; Doche C; Dunkelman O; Fitzi M; Fouque PA; Fournier JJA; Fujisaki K; Fujisaki E; Furukawa J; Galindo D; Halevi S; Handschuh H; Heneghan C; Holenstein T; Hoshino F; Hwang YH; Isshiki T; Jochemsz E; Joux A; Juels A; Jutla C; Kiayias A; Kikuchi H; Kobayashi T; Kohno T; Krawczyk H; Kumar S; Lange T; Lee JW; Masucci B; May A; Mihaljevic M; Minematsu K; Monrose F; Montague P; Myers S; Naccache D; Nicolosi A; Obana S; Okazaki S; Okeya K; Olivier F; Oyono R; Page D; Park JH; Peng K; Pietrzak K; Raub D; Sakai Y; Sakurai K; Schindler W; Seo JW; Shin JH; Shparlinski I; Steinfeld R; Szydlo M; Kalai YT; Teranishi I; Tokita T; Tunstall M; Vercauteren F; Villegas K; Walfish S; Wang H; Wang X; Warinschi B; De Weger B; Wolf C; Yampolskiy A; Yang YH; Yin YL; Yoon J; Pointcheval D, 2006, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics): Preface

Everest G; van der Poorten A; Shparlinski I; Ward T, 2003, Recurrence Sequences, American Mathematical Society, http://dx.doi.org/10.1090/surv/104

Boztaş S; Shparlinski IE, 2001, Preface

Konyagin S; Shparlinski I, 1999, Character Sums with Exponential Functions and their Applications, Cambridge University Press, http://dx.doi.org/10.1017/cbo9780511542930

Shparlinski I, 1999, Number Theoretic Methods in Cryptography, Birkhäuser Basel, http://dx.doi.org/10.1007/978-3-0348-8664-2

Shparlinski IE, 1999, Finite Fields: Theory and Computation, Springer Netherlands, http://dx.doi.org/10.1007/978-94-015-9239-0

Shparlinski IE, 1992, Computational and Algorithmic Problems in Finite Fields, Springer Netherlands, http://dx.doi.org/10.1007/978-94-011-1806-4

Konyagin SV; Shparlinski IE; Vyugin IV, 2022, 'Polynomial Equations in Subgroups and Applications', in Analysis at Large, Springer International Publishing, pp. 273 - 297, http://dx.doi.org/10.1007/978-3-031-05331-3_12

Cools R; Kuo FY; Sloan IH; Nuyens D, 2020, 'Lattice algorithms for multivariate approximation in periodic spaces with general weight parameters', in Brenner SC; Shparlinski I; Shu C-W; Szyld D (ed.), 75 Years of Mathematics of Computation, American Mathematical Society, pp. 93 - 113, http://dx.doi.org/10.1090/conm/754/15150

Kaszian J; Moree P; Shparlinski I, 2018, 'Periodic structure of the exponential pseudorandom number generator', in Larcher G; Pillichshammer F; Winterhof A; Xing C (ed.), Applied Algebra and Number Theory, Cambridge University Press, pp. 190 - 203, http://dx.doi.org/10.1017/CCO9781139696456.011

Ostafe A; Shparlinski IE, 2017, 'Orbits of algebraic dynamical systems in subgroups and subfields', in Elsholtz C; Grabner P (ed.), Number Theory - Diophantine Problems, Uniform Distribution and Applications: Festschrift in Honour of Robert F. Tichy's 60th Birthday, Springer, pp. 347 - 368, http://dx.doi.org/10.1007/978-3-319-55357-3_18

Kaszián J; Moree P; Shparlinski IE, 2014, 'Periodic structure of the exponential pseudorandom number generator', in Applied Algebra and Number Theory, Cambridge University Press, pp. 190 - 203, http://dx.doi.org/10.1017/cbo9781139696456.012

Shparlinski IE, 2013, 'Additive Combinatorics over Finite Fields: New Results and Applications', in Finite Fields and Their Applications, DE GRUYTER, pp. 233 - 272, http://dx.doi.org/10.1515/9783110283600.233

Cillerueloa J; Lucab F; Shparlinskic IE, 2011, 'Power values of palindromes', in Frontiers of Combinatorics and Number Theory, pp. 103 - 110

Shparlinski I, 2011, 'Computational Diffie-Hellman Problem', in Encyclopedia of Cryptography and Security, Springer US, pp. 240 - 244, http://dx.doi.org/10.1007/978-1-4419-5906-5_882

Murty R; Shparlinski I, 2007, 'GROUP STRUCTURE OF ELLIPTIC CURVES OVER FINITE FIELDS AND APPLICATIONS', in Garcia A; Stichtenoth H (ed.), TOPICS IN GEOMETRY, CODING THEORY AND CRYPTOGRAPHY, SPRINGER, pp. 167 - 198, http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000267348300005&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Shparlinski I, 2003, '1/M Generator', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 279 - 282, http://dx.doi.org/10.1007/978-3-0348-8037-4_26

Shparlinski I, 2003, 'Approximation of the Discrete Logarithm Modulo p — 1', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 123 - 128, http://dx.doi.org/10.1007/978-3-0348-8037-4_10

Shparlinski I, 2003, 'Approximation of the Discrete Logarithm Modulo p', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 109 - 122, http://dx.doi.org/10.1007/978-3-0348-8037-4_9

Shparlinski I, 2003, 'Approximation of the Discrete Logarithm by Boolean Functions', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 129 - 141, http://dx.doi.org/10.1007/978-3-0348-8037-4_11

Shparlinski I, 2003, 'Approximation of the Discrete Logarithm by Real Polynomials', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 143 - 156, http://dx.doi.org/10.1007/978-3-0348-8037-4_12

Shparlinski I, 2003, 'Arithmetic Functions', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 67 - 81, http://dx.doi.org/10.1007/978-3-0348-8037-4_6

Shparlinski I, 2003, 'Basic Notation and Definitions', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 17 - 26, http://dx.doi.org/10.1007/978-3-0348-8037-4_2

Shparlinski I, 2003, 'Bit Security of NTRU', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 223 - 229, http://dx.doi.org/10.1007/978-3-0348-8037-4_21

Shparlinski I, 2003, 'Bit Security of the Diffie—Hellman Secret Key', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 189 - 194, http://dx.doi.org/10.1007/978-3-0348-8037-4_15

Shparlinski I, 2003, 'Bit Security of the RSA Encryption and the Shamir Message Passing Scheme', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 211 - 215, http://dx.doi.org/10.1007/978-3-0348-8037-4_19

Shparlinski I, 2003, 'Bit Security of the XTR and LUC Secret Keys', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 217 - 221, http://dx.doi.org/10.1007/978-3-0348-8037-4_20

Shparlinski I, 2003, 'Boolean Complexity of the Diffie-Hellman Secret Key', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 179 - 188, http://dx.doi.org/10.1007/978-3-0348-8037-4_14

Shparlinski I, 2003, 'Complexity Theory', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 103 - 106, http://dx.doi.org/10.1007/978-3-0348-8037-4_8

Shparlinski I, 2003, 'Concluding Remarks and Open Questions', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 341 - 365, http://dx.doi.org/10.1007/978-3-0348-8037-4_33

Shparlinski I, 2003, 'Distribution and Discrepancy', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 61 - 65, http://dx.doi.org/10.1007/978-3-0348-8037-4_5

Shparlinski I, 2003, 'Distribution of the ElGamal Signature', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 207 - 210, http://dx.doi.org/10.1007/978-3-0348-8037-4_18

Shparlinski I, 2003, 'Distribution of the RSA and Exponential Pairs', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 231 - 237, http://dx.doi.org/10.1007/978-3-0348-8037-4_22

Shparlinski I, 2003, 'Exponential Sums', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 37 - 60, http://dx.doi.org/10.1007/978-3-0348-8037-4_4

Shparlinski I, 2003, 'Exponentiation and Inversion with Precomputation', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 239 - 245, http://dx.doi.org/10.1007/978-3-0348-8037-4_23

Shparlinski I, 2003, 'Introduction', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 1 - 14, http://dx.doi.org/10.1007/978-3-0348-8037-4_1

Shparlinski I, 2003, 'Inversive, Polynomial and Quadratic Exponential Generators', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 283 - 294, http://dx.doi.org/10.1007/978-3-0348-8037-4_27

Shparlinski I, 2003, 'Lattices and the Hidden Number Problem', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 83 - 102, http://dx.doi.org/10.1007/978-3-0348-8037-4_7

Shparlinski I, 2003, 'Naor—Reingold Function', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 271 - 277, http://dx.doi.org/10.1007/978-3-0348-8037-4_25

Shparlinski I, 2003, 'Polynomial Approximation and Arithmetic Complexity of the Diffie-Hellman Secret Key', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 159 - 177, http://dx.doi.org/10.1007/978-3-0348-8037-4_13

Shparlinski I, 2003, 'Polynomial Approximation, Permanents and Noisy Exponentiation in Finite Fields', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 325 - 332, http://dx.doi.org/10.1007/978-3-0348-8037-4_31

Shparlinski I, 2003, 'Polynomials and Recurrence Sequences', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 27 - 36, http://dx.doi.org/10.1007/978-3-0348-8037-4_3

Shparlinski I, 2003, 'RSA and Blum—Blum—Shub Generators', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 249 - 270, http://dx.doi.org/10.1007/978-3-0348-8037-4_24

Shparlinski I, 2003, 'Security Against the Cycling Attack on the RSA and Timed-release Crypto', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 197 - 200, http://dx.doi.org/10.1007/978-3-0348-8037-4_16

Shparlinski I, 2003, 'Special Polynomials and Boolean Functions', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 333 - 339, http://dx.doi.org/10.1007/978-3-0348-8037-4_32

Shparlinski I, 2003, 'Square-Freeness Testing and Other Number-Theoretic Problems', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 303 - 308, http://dx.doi.org/10.1007/978-3-0348-8037-4_29

Shparlinski I, 2003, 'Subset Sum Generators', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 295 - 299, http://dx.doi.org/10.1007/978-3-0348-8037-4_28

Shparlinski I, 2003, 'The Insecurity of the Digital Signature Algorithm with Partially Known Nonces', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 201 - 206, http://dx.doi.org/10.1007/978-3-0348-8037-4_17

Shparlinski I, 2003, 'Trade-off Between the Boolean and Arithmetic Depths of Modulo p Functions', in Cryptographic Applications of Analytic Number Theory, Birkhäuser Basel, pp. 309 - 323, http://dx.doi.org/10.1007/978-3-0348-8037-4_30

Shparlinski IE, 2002, 'EXPONENTIAL SUMS IN CODING THEORY, CRYPTOLOGY AND ALGORITHMS', in Coding Theory and Cryptology, CO-PUBLISHED WITH SINGAPORE UNIVERSITY PRESS, pp. 323 - 383, http://dx.doi.org/10.1142/9789812388841_0009

von zur Gathen J; Shparlinski I, 2001, 'Gauß Periods in Finite Fields', in Finite Fields and Applications, Springer Berlin Heidelberg, pp. 162 - 177, http://dx.doi.org/10.1007/978-3-642-56755-1_14

Friedlander JB; Lieman D; Shparlinski IE, 1999, 'On the Distribution of the RSA Generator', in Sequences and their Applications, Springer London, pp. 205 - 212, http://dx.doi.org/10.1007/978-1-4471-0551-0_14

Mullen GL; Shparlinski I, 1996, 'Open problems and conjectures in finite fields', in Finite Fields and Applications, Cambridge University Press, pp. 243 - 268, http://dx.doi.org/10.1017/cbo9780511525988.021

Shparlinski I, 1996, 'Approximate constructions in finite fields', in Finite Fields and Applications, Cambridge University Press, pp. 313 - 332, http://dx.doi.org/10.1017/cbo9780511525988.024

Shparlinski IE, 1995, 'On Some Characteristics of Uniformity of Distribution and Their Applications', in Computational Algebra and Number Theory, Springer Netherlands, pp. 227 - 241, http://dx.doi.org/10.1007/978-94-017-1108-1_16

Shparlinski IE, 'Diffie–Hellman Problem', in Encyclopedia of Cryptography and Security, Springer US, pp. 154 - 158, http://dx.doi.org/10.1007/0-387-23483-7_112

Shparlinski I; Brenner SC; Shu C-W; Szyld DB, (eds.), 2020, 75 Years of Mathematics of Computation, American Mathematical Society, https://bookstore.ams.org/conm-754

Bag N; Shparlinski IE, 2023, 'Bounds on bilinear sums of Kloosterman sums', Journal of Number Theory, vol. 242, pp. 102 - 111, http://dx.doi.org/10.1016/j.jnt.2022.07.006

Chen C; Kerr B; Maynard J; Shparlinski IE, 2023, 'Metric theory of Weyl sums', Mathematische Annalen, vol. 385, pp. 309 - 355, http://dx.doi.org/10.1007/s00208-021-02352-x

Dąbrowski A; Pomykała J; Shparlinski IE, 2023, 'On oracle factoring of integers', Journal of Complexity, pp. 101741 - 101741, http://dx.doi.org/10.1016/j.jco.2023.101741

Kaminski M; Shparlinski IE; Waldschmidt M, 2023, 'On sets of linear forms of maximal complexity', Computational Complexity, vol. 32, http://dx.doi.org/10.1007/s00037-022-00234-5

Shparlinski IE, 2023, 'On the Glasner property for matrices with polynomial entries', Journal of Number Theory, vol. 242, pp. 522 - 531, http://dx.doi.org/10.1016/j.jnt.2022.04.015

Shparlinski IE; Thuswaldner JM, 2023, 'Weyl Sums over Integers with Digital Restrictions', Michigan Mathematical Journal, vol. -1, http://dx.doi.org/10.1307/mmj/20216094

Bagshaw C; Shparlinski IE, 2022, 'Energy bounds, bilinear forms and their applications in function fields', Finite Fields and their Applications, vol. 82, pp. 102048 - 102048, http://dx.doi.org/10.1016/j.ffa.2022.102048

Baker RC; Chen C; Shparlinski IE, 2022, 'Large Weyl sums and Hausdorff dimension', Journal of Mathematical Analysis and Applications, vol. 510, pp. 1 - 46, http://dx.doi.org/10.1016/j.jmaa.2022.126030

Baker RC; Chen C; Shparlinski IE, 2022, 'Large Weyl sums and Hausdorff dimension', Journal of Mathematical Analysis and Applications, vol. 510, pp. 126030 - 126030, http://dx.doi.org/10.1016/j.jmaa.2022.126030

Baker RC; Munsch M; Shparlinski IE, 2022, 'Additive energy and a large sieve inequality for sparse sequences', Mathematika, vol. 68, pp. 362 - 399, http://dx.doi.org/10.1112/mtk.12140

Banks W; Shparlinski I, 2022, 'On a conjecture of Soundararajan', Bulletin of the London Mathematical Society, vol. 54, pp. 301 - 317, http://dx.doi.org/10.1112/blms.12524

Ghioca D; Ostafe A; Saleh S; Shparlinski IE, 2022, 'On sparsity of representations of polynomials as linear combinations of exponential functions', Journal of the London Mathematical Society, http://dx.doi.org/10.1112/jlms.12554

Ghioca D; Shparlinski IE, 2022, 'Order of torsion for reduction of linearly independent points for a family of Drinfeld modules', Journal of Number Theory, vol. 233, pp. 112 - 125, http://dx.doi.org/10.1016/j.jnt.2021.06.006

Ostafe A; Shparlinski IE, 2022, 'On the Skolem problem and some related questions for parametric families of linear recurrence sequences', Canadian Journal of Mathematics, vol. 74, pp. 773 - 792, http://dx.doi.org/10.4153/S0008414X21000080

Ostafe A; Shparlinski IE; Pottmeyer L, 2022, 'Perfect powers in value sets and orbits of polynomials', The New York Journal of Mathematics

Ostafe A; Shparlinski IE; Voloch JF, 2022, 'Equations and Character Sums with Matrix Powers, Kloosterman Sums over Small Subgroups, and Quantum Ergodicity', INTERNATIONAL MATHEMATICS RESEARCH NOTICES, http://dx.doi.org/10.1093/imrn/rnac226

Shkredov ID; Shparlinski IE; Zaharescu A, 2022, 'Bilinear Forms With Modular Square Roots and Twisted Second Moments of Half Integral Weight Dirichlet Series', International Mathematics Research Notices, vol. 2022, pp. 17431 - 17474, http://dx.doi.org/10.1093/imrn/rnab220

Shparlinski IE, 2022, 'Bilinear sums of Gauss sums', Acta Arithmetica, vol. 202, pp. 379 - 388, http://dx.doi.org/10.4064/aa210523-3-2

Shparlinski IE, 2022, 'MULTIPLICATIVE PROPERTIES of HILBERT CUBES', SIAM Journal on Discrete Mathematics, vol. 36, pp. 1064 - 1070, http://dx.doi.org/10.1137/22M1470396

Bag N; Shparlinski IE, 2021, 'Bounds of some double exponential sums', Journal of Number Theory, vol. 219, pp. 228 - 236, http://dx.doi.org/10.1016/j.jnt.2020.09.020

Baker RC; Chen C; Shparlinski IE, 2021, 'Bounds on the Norms of Maximal Operators on Weyl Sums', , http://arxiv.org/abs/2107.13674v1

Baker RC; Munsch M; Shparlinski IE, 2021, 'Additive energy and a large sieve inequality for sparse sequences', , http://arxiv.org/abs/2103.12659v2

Chen C; Shparlinski IE, 2021, 'Hybrid Bounds on Two-Parametric Families of Weyl Sums Along Smooth Curves', Michigan Mathematical Journal, vol. -1, http://dx.doi.org/10.1307/mmj/20205904

Chen C; Shparlinski IE, 2021, 'Small values of Weyl sums', Journal of Mathematical Analysis and Applications, vol. 495, http://dx.doi.org/10.1016/j.jmaa.2020.124743

Ghioca D; Ostafe A; Saleh S; Shparlinski IE, 2021, 'A SPARSITY RESULT for the DYNAMICAL MORDELL-LANG CONJECTURE in POSITIVE CHARACTERISTIC', Bulletin of the Australian Mathematical Society, vol. 104, pp. 381 - 390, http://dx.doi.org/10.1017/S0004972721000083

Karpinski M; Shparlinski IE, 2021, 'Noisy polynomial interpolation modulo prime powers', Journal of Complexity, vol. 64, http://dx.doi.org/10.1016/j.jco.2020.101542

Kerr B; Mello J; Shparlinski IE, 2021, 'On elements of large order on elliptic curves and multiplicative dependent images of rational functions over finite fields', Illinois Journal of Mathematics, vol. 65, pp. 499 - 514, http://dx.doi.org/10.1215/00192082-9043478

Kerr B; Mérai L; Shparlinski I, 2021, 'On digits of Mersenne numbers', Revista Matemática Iberoamericana, vol. 38, pp. 1901 - 1925, http://dx.doi.org/10.4171/rmi/1316

Kerr B; Shkredov ID; Shparlinski IE; Zaharescu A, 2021, 'Energy bounds for modular roots and their applications', , http://arxiv.org/abs/2103.09405v1

Mérai L; Ostafe A; Shparlinski IE, 2021, 'Dynamical irreducibility of polynomials modulo primes', Mathematische Zeitschrift, vol. 298, pp. 1187 - 1199, http://dx.doi.org/10.1007/s00209-020-02630-5

Mérai L; Shparlinski IE, 2021, 'On the dynamical system generated by the Möbius transformation at prime times', Research in Mathematical Sciences, vol. 8, http://dx.doi.org/10.1007/s40687-021-00249-4

Ostafe A; Pottmeyer L; Shparlinski IE, 2021, 'Perfect powers in value sets and orbits of polynomials', NEW YORK JOURNAL OF MATHEMATICS, vol. 27, pp. 903 - 917, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000669490500001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Ostafe A; Pottmeyer L; Shparlinski IE, 2021, 'Perfect powers in value sets and orbits of polynomials', New York Journal of Mathematics, vol. 27, pp. 903 - 917

Ostafe A; Shparlinski IE, 2021, 'Additive energy of cyclic matrix groups and character sums with matrix exponential functions', , http://arxiv.org/abs/2108.13146v2

Sha M; Shparlinski IE, 2021, 'Möbius Randomness Law for Frobenius Traces of Ordinary Curves', Canadian Mathematical Bulletin, vol. 64, pp. 192 - 203, http://dx.doi.org/10.4153/S0008439520000363

Shparlinski IE, 2021, 'Bounds of trilinear sums with Kloosterman fractions', Archiv der Mathematik, vol. 117, pp. 261 - 266, http://dx.doi.org/10.1007/s00013-021-01623-y

Shparlinski IE, 2021, 'On the arithmetic structure of rational numbers in the cantor set', Bulletin of the Australian Mathematical Society, vol. 103, pp. 22 - 27, http://dx.doi.org/10.1017/S0004972720000386

Shparlinski IE; Stewart CL, 2021, 'Counting solvable s-unit equations', Proceedings of the American Mathematical Society, vol. 149, pp. 5119 - 5129, http://dx.doi.org/10.1090/proc/15674

Shparlinski IE; Thuswaldner JM, 2021, 'Weyl sums over integers with digital restrictions', , http://arxiv.org/abs/2105.04835v1

Shparlinski IE; Voloch JF, 2021, 'Erratum: Value sets of sparse polynomials (Canadian Mathematical Bulletin (2020) 63 (187-196) DOI: 10.4153/xxxx)', Canadian Mathematical Bulletin, pp. 1 - 3, http://dx.doi.org/10.4153/S0008439521000928

Shparlinski IE; Wang Q, 2021, 'Exponential sums with sparse polynomials over finite fields', SIAM Journal on Discrete Mathematics, vol. 35, pp. 976 - 987, http://dx.doi.org/10.1137/20M1357731

Banks W; Shparlinski I, 2020, 'Congruences with intervals and arbitrary sets', Archiv der Mathematik, vol. 114, pp. 527 - 539, http://dx.doi.org/10.1007/s00013-019-01421-7

Brandes J; Shparlinski IE, 2020, 'Two-dimensional Weyl sums failing square-root cancellation along lines', , http://arxiv.org/abs/2012.08877v1

Chen C; Kerr B; Maynard J; Shparlinski I, 2020, 'Metric theory of Weyl sums', , http://arxiv.org/abs/2011.09306v1

Chen C; Kerr B; Shparlinski I, 2020, 'Metric theory of lower bounds on Weyl sums', , http://arxiv.org/abs/2004.02539v3

Chen C; Shparlinski IE, 2020, 'Hausdorff dimension of the large values of Weyl sums', Journal of Number Theory, vol. 214, pp. 27 - 37, http://dx.doi.org/10.1016/j.jnt.2020.04.023

Chen C; Shparlinski IE, 2020, 'Hybrid bounds on two-parametric family Weyl sums along smooth curves', , http://arxiv.org/abs/2003.02419v1

Chen C; Shparlinski IE, 2020, 'On large values of Weyl sums', Advances in Mathematics, vol. 370, http://dx.doi.org/10.1016/j.aim.2020.107216

Di Benedetto D; Garaev MZ; Garcia VC; Gonzalez-Sanchez D; Shparlinski IE; Trujillo CA, 2020, 'New estimates for exponential sums over multiplicative subgroups and intervals in prime fields', Journal of Number Theory, vol. 215, pp. 261 - 274, http://dx.doi.org/10.1016/j.jnt.2020.02.004

Dunn A; Kerr B; Shparlinski IE; Zaharescu A, 2020, 'Bilinear forms in Weyl sums for modular square roots and applications', Advances in Mathematics, vol. 375, http://dx.doi.org/10.1016/j.aim.2020.107369

Gómez-Pérez D; Mérai L; Shparlinski IE, 2020, 'On the complexity of exact counting of dynamically irreducible polynomials', Journal of Symbolic Computation, vol. 99, pp. 231 - 241, http://dx.doi.org/10.1016/j.jsc.2019.06.001

Kerr B; Mello J; Shparlinski I, 2020, 'An effective local-global principle for algebraic varieties and the sum product problem in finite fields', , http://arxiv.org/abs/2005.02923v3

Kerr B; Mérai L; Shparlinski IE, 2020, 'On digits of Mersenne numbers', , http://arxiv.org/abs/2001.03380v4

Kerr B; Shparlinski IE, 2020, 'Bilinear sums of Kloosterman sums, multiplicative congruences and average values of the divisor function over families of arithmetic progressions', Research in Number Theory, vol. 6, http://dx.doi.org/10.1007/s40993-020-0191-9

Konyagin SV; Makarychev SV; Shparlinski IE; Vyugin IV, 2020, 'On the Structure of Graphs of Markoff Triples', Quarterly Journal of Mathematics, vol. 71, pp. 637 - 648, http://dx.doi.org/10.1093/qmathj/haz055

Konyagin SV; Shparlinski IE; Vyugin IV, 2020, 'Polynomial Equations in Subgroups and Applications', , http://arxiv.org/abs/2005.05315v1

Korolev M; Shparlinski I, 2020, 'Sums of algebraic trace functions twisted by arithmetic functions', Pacific Journal of Mathematics, vol. 304, pp. 505 - 522, http://dx.doi.org/10.2140/pjm.2020.304.505

Li R; Shparlinski IE, 2020, 'Effective bounds on multiplicatively dependent orbits of integer polynomials modulo S-integers', , http://arxiv.org/abs/2001.09721v1

Liu K; Shparlinski IE; Zhang T, 2020, 'Average distribution of k-free numbers in arithmetic progressions', Mathematische Nachrichten, vol. 293, pp. 1505 - 1514, http://dx.doi.org/10.1002/mana.201900006

Macourt S; Petridis G; Shkredov ID; Shparlinski IE, 2020, 'BOUNDS of TRILINEAR and TRINOMIAL EXPONENTIAL SUMS', SIAM Journal on Discrete Mathematics, vol. 34, pp. 2124 - 2136, http://dx.doi.org/10.1137/20M1325502

Munsch M; Shparlinski IE, 2020, 'Smooth squarefree and square-full integers in arithmetic progressions', Journal of the London Mathematical Society, vol. 101, pp. 1941 - 1067, http://dx.doi.org/10.1112/jlms.12297

Mérai L; Shparlinski IE, 2020, 'Distribution of short subsequences of inversive congruential pseudorandom numbers modulo $2^t$', Mathematics of Computation, vol. 322, pp. 911 - 922, http://dx.doi.org/10.1090/mcom/3467

Mérai L; Shparlinski IE, 2020, 'Unlikely intersections over finite fields: Polynomial orbits in small subgroups', Discrete and Continuous Dynamical Systems- Series A, vol. 40, pp. 1065 - 1073, http://dx.doi.org/10.3934/dcds.2020070

Pakovich F; Shparlinski IE, 2020, 'Level curves of rational functions nd unimodular points on rational curves', Proceedings of the American Mathematical Society, vol. 148, pp. 1829 - 1833, http://dx.doi.org/10.1090/proc/14928

Ricotta G; Royer E; Shparlinski I, 2020, 'Kloosterman paths of prime powers moduli, II', Bulletin de la Societe Mathematique de France, vol. 148, pp. 173 - 188, http://dx.doi.org/10.24033/bsmf.2802

Shkredov ID; Shparlinski IE; Zaharescu A, 2020, 'On the distribution of modular square roots of primes', , http://arxiv.org/abs/2009.03460v1

Shparlinski I, 2020, 'Lower bounds for periods of Ducci sequences', Bulletin of the Australian Mathematical Society, vol. 102, pp. 31 - 38, http://dx.doi.org/10.1017/S0004972719001187

Shparlinski I, 2020, 'Unlikely intersections over finite fields: polynomial orbits in small subgroups', DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS., Ser.A, vol. 40, pp. 1065 - 1073, http://dx.doi.org/10.3934/dcds.2020070

Shparlinski I; Banks W, 2020, 'Congruences with intervals and arbitrary sets', Archiv der Mathematik, vol. 114, pp. 527 - 539, http://dx.doi.org/10.1007/s00013-019-01421-7

Shparlinski I; Banks W, 2020, 'Sums with the Mobius function twisted by characters with powerful moduli', Trans. Amer. Math. Soc., pp. 249 - 272, http://dx.doi.org/10.1090/tran/7914

Shparlinski I; Chen C, 2020, 'Hausdorff dimension of the large values of Weyl sums', Journal of Number Theory, pp. 27 - 37, http://dx.doi.org/10.1016/j.jnt.2020.04.023

Shparlinski I; Chen C, 2020, 'On large values of Weyl sums', Advances in Mathematics, vol. 370, pp. 1 - 48, http://dx.doi.org/10.1016/j.aim.2020.107216

Shparlinski I; Dunn A; Kerr B; Zaharescu A, 2020, 'Bilinear forms in Weyl sums for modular square roots and applications', Advances in Mathematics, vol. 375, pp. 1 - 58, http://dx.doi.org/10.1016/j.aim.2020.107369

Shparlinski I; Gomez-Perez D; Merai L, 2020, 'On the complexity of exact counting of dynamically irreducible polynomials', Journal of Symbolic Computation, vol. 99, pp. 231 - 241, http://dx.doi.org/10.1016/j.jsc.2019.06.001

Shparlinski I; Kerr B, 2020, 'Bilinear sums of Kloosterman sums, multiplicative congruences and average values of the divisor function over families of arithmetic progressions', Research in Number Theory, pp. 1 - 21, http://dx.doi.org/10.1007/s40993-020-0191-9

Shparlinski I; Kerr B; Yau KH, 2020, 'A refinement of the Burgess bound for character sums', Michigan Mathematical Journal, vol. 69, pp. 227 - 240, http://dx.doi.org/10.1307/mmj/1573700737

Shparlinski I; Korolev M, 2020, 'Sums of algebraic trace functions twisted by arithmetic functions.', Pacific J. Math., vol. 304, pp. 505 - 18, http://dx.doi.org/10.2140/pjm.2020.304.505

Shparlinski I; Pakovich F, 2020, 'Level curves of rational functions and unimodular points on rational curves.', Proceedings of the American Mathematical Society, vol. 148, pp. 1829 - 1833, http://dx.doi.org/10.1090/proc/14928

Shparlinski I; Voloch F, 2020, 'Binomial exponential sums', Annali della Scuola Normale Superiore di Pisa: Classe di Scienze, vol. 21, pp. 931 - 941, http://dx.doi.org/10.2422/2036-2145.201811_007

Shparlinski I; Voloch F, 2020, 'Value sets of sparse polynomials', Canad. Math. Bull., vol. 63, pp. . 187 - 196, http://dx.doi.org/10.4153/S0008439519000316

Shparlinski IE, 2020, 'Geometric progressions in vector sumsets over finite fields', Finite Fields and their Applications, vol. 68, http://dx.doi.org/10.1016/j.ffa.2020.101747

Shparlinski IE, 2020, 'Orders of points in families of elliptic curves', Proceedings of the American Mathematical Society, vol. 148, pp. 2371 - 2377, http://dx.doi.org/10.1090/proc/14901

Shparlinski IE; Stewart CL, 2020, 'Counting solvable $S$-unit equations', , http://arxiv.org/abs/2007.15170v1

Shparlinski IE; Technau M, 2020, 'Kloosterman sums with twice-differentiable functions', Functiones et Approximatio Commentarii Mathematici, vol. 63, pp. 113 - 124, http://dx.doi.org/10.7169/facm/1845

Shparlinski IE; Voloch JF, 2020, 'Value Sets of Sparse Polynomials', Canadian Mathematical Bulletin, vol. 63, pp. 187 - 196, http://dx.doi.org/10.4153/S0008439519000316

Banks WD; Friedlander JB; Pomerance C; Shparlinski IE, 2019, 'Counting integers with a smooth totient', The Quarterly Journal of Mathematics, pp. 1371 - 1386, http://dx.doi.org/10.1093/qmathj/haz026

Banks WD; Shparlinski IE, 2019, 'Bounds on short character sums and L-functions with characters to a powerful modulus', Journal d'Analyse Mathematique, vol. 139, pp. 239 - 263, http://dx.doi.org/10.1007/s11854-019-0060-4

Bordellès O; Dai L; Heyman R; Pan H; Shparlinski IE, 2019, 'On a sum involving the Euler function', Journal of Number Theory, vol. 202, pp. 278 - 297, http://dx.doi.org/10.1016/j.jnt.2019.01.006

Bretèche RDL; Kurlberg P; Shparlinski IE, 2019, 'On the number of products which form perfect powers and discriminants of multiquadratic extensions', International Mathematics Research Notices, http://dx.doi.org/10.1093/imrn/rnz316

Breuer F; Shparlinski IE, 2019, 'Lower bounds for periods of Ducci sequences', Bull. Aust. Math. Soc., http://dx.doi.org/10.1017/S0004972719001187

Bérczes A; Ostafe A; Shparlinski IE; Silverman JH, 2019, 'Multiplicative Dependence Among Iterated Values of Rational Functions Modulo Finitely Generated Groups', International Mathematics Research Notices, http://dx.doi.org/10.1093/imrn/rnz091

Chen C; Shparlinski IE, 2019, 'New bounds of Weyl sums', International Mathematics Research Notices, http://dx.doi.org/10.1093/imrn/rnz293

Dietmann R; Ostafe A; Shparlinski IE, 2019, 'Discriminants of Fields Generated by Polynomials of Given Height', , http://arxiv.org/abs/1909.00135v2

El Abdalaoui EH; Shparlinski IE, 2019, 'Disjointness of the Möbius Transformation and Möbius Function', Research in the Mathematical Sciences, vol. 6, http://dx.doi.org/10.1007/s40687-019-0180-6

Konyagin SV; Sha M; Shparlinski IE; Stewart CL, 2019, 'On the distribution of multiplicatively dependent vectors', , http://arxiv.org/abs/1903.09796v4

Liu K; Shparlinski IE; Zhang T, 2019, 'CANCELLATIONS BETWEEN KLOOSTERMAN SUMS MODULO A PRIME POWER WITH PRIME ARGUMENTS', Mathematika, vol. 65, pp. 475 - 487, http://dx.doi.org/10.1112/s0025579318000554

Macourt S; Shparlinski IE, 2019, 'Double sums of Kloosterman sums in finite fields', Finite Fields and their Applications, vol. 60, http://dx.doi.org/10.1016/j.ffa.2019.101575

Mérai L; Shparlinski IE, 2019, 'Sparsity of curves and additive and multiplicative expansion of rational maps over finite fields', Acta Arithmetica, vol. 188, pp. 401 - 411, http://dx.doi.org/10.4064/aa180307-20-8

Ostafe A, 2019, 'Polynomial Values in Affine Subspaces of Finite Fields', Journal d'Analyse Mathematique, pp. 49 - 81, http://dx.doi.org/10.1007/s11854-019-0021-y

Petridis G; Shparlinski IE, 2019, 'Bounds on trilinear and quadrilinear exponential sums', Journal d'Analyse Mathématique, http://arxiv.org/abs/1604.08469v4

Roche-Newton O; Shparlinski IE; Winterhof A, 2019, 'Analogues of the Balog–Wooley Decomposition for Subsets of Finite Fields and Character Sums with Convolutions', Annals of Combinatorics, http://dx.doi.org/10.1007/s00026-019-00420-3

SHPARLINSKI IGORE, 2019, 'ON FINDING SOLUTIONS TO EXPONENTIAL CONGRUENCES', Bulletin of the Australian Mathematical Society, pp. 1 - 4, http://dx.doi.org/10.1017/s0004972718001302

Sha M; Shparlinski IE, 2019, 'Möbius Randomness Law for Frobenius Traces', , http://arxiv.org/abs/1909.00969v3

Shparlinski I, 2019, 'The Sato-Tate distribution in thin families of elliptic curves over high degree extensions of finite fields', International Journal of Number Theory, vol. 15, pp. 469 - 477, http://dx.doi.org/10.1142/S1793042119500246

Shparlinski I; Zannier U, 2019, 'Arithmetic properties of quadratic exponential polynomials', New York Journal of Mathematics, vol. 25, pp. 207 - 218, https://www.emis.de/journals/NYJM/nyjm/j/2019/25-12p.pdf

Shparlinski IE, 2019, 'Bilinear Forms with Kloosterman and Gauss Sums', TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, http://dx.doi.org/10.1090/tran/7506

Shparlinski IE, 2019, 'Bounds on average values of double incomplete Kloosterman sums', Journal of Number Theory, vol. 203, pp. 1 - 11, http://dx.doi.org/10.1016/j.jnt.2019.03.009

Shparlinski IE, 2019, 'ON SHORT PRODUCTS OF PRIMES IN ARITHMETIC PROGRESSIONS', Proceedings of the American Mathematical Society, vol. 147, pp. 977 - 986, http://dx.doi.org/10.1090/proc/14289

Shparlinski IE; Voloch JF, 2019, 'Binomial exponential sums', ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA - CLASSE DI SCIENZE, pp. 1 - 1, http://dx.doi.org/10.2422/2036-2145.201811_007

Banks WD; Guo VZ; Shparlinski IE, 2018, 'Some arithmetic properties of numbers of the form $\lfloor p^c\rfloor$', Indagationes Mathematicae, vol. 27, pp. 423 - 436, http://dx.doi.org/10.1016/j.indag.2015.10.002

Bordellès O; Luca F; Moree P; Shparlinski IE, 2018, 'DENOMINATORS of BERNOULLI POLYNOMIALS', Mathematika, vol. 64, pp. 519 - 541, http://dx.doi.org/10.1112/S0025579318000153

Bordellès O; Luca F; Shparlinski IE, 2018, 'On the error term of a lattice counting problem', Journal of Number Theory, vol. 182, pp. 19 - 36, http://dx.doi.org/10.1016/j.jnt.2017.07.019

Bourgain J; Garaev MZ; Konyagin SV; Shparlinski IE, 2018, 'Multiplicative congruences with variables from short intervals', Journal d'Analyse Mathematique, vol. 124, pp. 117 - 147, http://dx.doi.org/10.1007/s11854-014-0029-2

Chang M-C; D'Andrea C; Ostafe A; Shparlinski IE; Sombra M, 2018, 'Orbits of Polynomial Dynamical Systems Modulo Primes', Proceedings of the American Mathematical Society, vol. 146, pp. 2015 - 2025, http://dx.doi.org/10.1090/proc/13904

Chang MC; Kerr B; Shparlinski IE, 2018, 'On the exponential large sieve inequality for sparse sequences modulo primes', Journal of Mathematical Analysis and Applications, vol. 459, pp. 53 - 81, http://dx.doi.org/10.1016/j.jmaa.2017.10.070

D'Andrea C; Ostafe A; Shparlinski IE; Sombra M, 2018, 'Reductions Modulo Primes of Systems of Polynomial Equations and Algebraic Dynamical Systems', Transactions of the American Mathematical Society, vol. 371, pp. 1169 - 1198, http://dx.doi.org/10.1090/tran/7437

D’Andrea C; Ostafe A; Shparlinski IE; Sombra M, 2018, 'Reductions modulo primes of systems of polynomial equations and algebraic dynamical systems', Transactions of the American Mathematical Society, vol. 371, pp. 1169 - 1198, http://dx.doi.org/10.1090/tran/7437

Gómez-Pérez D; Shparlinski IE, 2018, 'Arithmetic Properties of Integers in Chains and Reflections of g-ary Expansions', Experimental Mathematics, vol. 27, pp. 184 - 192, http://dx.doi.org/10.1080/10586458.2016.1239146

Heyman R; Shparlinski IE, 2018, 'On shifted Eisenstein polynomials', Periodica Mathematica Hungarica, vol. 69, pp. 170 - 181, http://dx.doi.org/10.1007/s10998-014-0061-0

Ivanyos G; Karpinski M; Santha M; Saxena N; Shparlinski IE, 2018, 'Polynomial Interpolation and Identity Testing from High Powers Over Finite Fields', Algorithmica, vol. 80, pp. 560 - 575, http://dx.doi.org/10.1007/s00453-016-0273-1

Karpinski M; Mérai L; Shparlinski IE, 2018, 'Identity testing and interpolation from high powers of polynomials of large degree over finite fields', Journal of Complexity, vol. 49, pp. 74 - 84, http://dx.doi.org/10.1016/j.jco.2018.07.006

LUCA F; RADZIWIŁŁ M; SHPARLINSKI IE, 2018, 'On the typical size and cancellations among the coefficients of some modular forms', Mathematical Proceedings of the Cambridge Philosophical Society, vol. 166, pp. 173 - 189, http://dx.doi.org/10.1017/S0305004117000780

Liu K; Shparlinski IE; Zhang T, 2018, 'Bilinear forms with exponential sums with binomials', Journal of Number Theory, vol. 188, pp. 172 - 185, http://dx.doi.org/10.1016/j.jnt.2017.12.011

Liu K; Shparlinski IE; Zhang T, 2018, 'Divisor problem in arithmetic progressions modulo a prime power', Advances in Mathematics, vol. 325, pp. 459 - 481, http://dx.doi.org/10.1016/j.aim.2017.12.006

Macourt S; Shkredov ID; Shparlinski IE, 2018, 'Multiplicative Energy of Shifted Subgroups and Bounds On Exponential Sums with Trinomials in Finite Fields', Canadian Journal of Mathematics, vol. 70, pp. 1319 - 1338, http://dx.doi.org/10.4153/CJM-2017-044-2

Ostafe A; Sha M; Shparlinski IE; Zannier U, 2018, 'On abelian multiplicatively dependent points on a curve in a torus', The Quarterly Journal of Mathematics, vol. 69, pp. 391 - 401, http://dx.doi.org/10.1093/qmath/hax045

Ostafe A; Sha M; Shparlinski IE; Zannier U, 2018, 'On multiplicative dependence of values of rational functions and a generalisation of the Northcott theorem', MICHIGAN MATHEMATICAL JOURNAL, vol. 5, https://arxiv.org/abs/1706.05874

Pappalardi F; Sha M; Shparlinski IE; Stewart CL, 2018, 'On multiplicatively dependent vectors of algebraic numbers', Transactions of the American Mathematical Society, vol. 370, pp. 6221 - 6244, http://dx.doi.org/10.1090/tran/7115

Pomerance C; Shparlinski I, 2018, 'CONNECTED COMPONENTS OF THE GRAPH GENERATED BY POWER MAPS IN PRIME FINITE FIELDS', Integers : Electronic Journal of Combinatorial Number Theory, vol. 18A, pp. 1 - 8, http://math.colgate.edu/~integers/vol18a.html

Sha M; Shparlinski IE, 2018, 'Effective results on linear dependence for elliptic curves', Pacific Journal of Mathematics, vol. 295, pp. 123 - 144, http://dx.doi.org/10.2140/pjm.2018.295.123

Sha M; Shparlinski IE, 2018, 'The Sato–Tate distribution in families of elliptic curves with a rational parameter of bounded height', Indagationes Mathematicae, vol. 28, pp. 306 - 320, http://dx.doi.org/10.1016/j.indag.2016.07.004

Shkredov ID; Shparlinski IE, 2018, 'Double Character Sums with Intervals and Arbitrary Sets', Proceedings of the Steklov Institute of Mathematics, vol. 303, pp. 239 - 258, http://dx.doi.org/10.1134/S0081543818080199

Shparlinski I; Voloch JF, 2018, 'Generators of Elliptic Curves over Finite Fields', Bulletin of the Institute of Mathematics Academia Sinica, vol. 9, pp. 657 - 670, https://web.ma.utexas.edu/users/voloch/Preprints/EC-Generators.pdf

Shparlinski IE, 2018, 'Character sums with smooth numbers', Archiv der Mathematik, vol. 110, pp. 467 - 476, http://dx.doi.org/10.1007/s00013-018-1168-y

Shparlinski IE, 2018, 'Constructing Dominating Sets in Circulant Graphs', Annals of Combinatorics, vol. 22, pp. 201 - 211, http://dx.doi.org/10.1007/s00026-018-0377-1

Shparlinski IE, 2018, 'Linear equations with rational fractions of bounded height and stochastic matrices', Quarterly Journal of Mathematics, vol. 69, pp. 487 - 499, http://dx.doi.org/10.1093/qmath/hax049

Shparlinski IE, 2018, 'Multiplicative orders in orbits of polynomials over finite fields', Glasgow Mathematical Journal, vol. 60, pp. 487 - 493, http://dx.doi.org/10.1017/S0017089517000222

Shparlinski IE, 2018, 'On Constructing Primitive Roots in Finite Fields With Advice', IEEE Transactions on Information Theory, vol. 64, pp. 7132 - 7136, http://dx.doi.org/10.1109/TIT.2018.2810938

Shparlinski IE, 2018, 'On the Győry-Sárközy-Stewart conjecture in function fields', Czechoslovak Mathematical Journal, vol. 68, pp. 1067 - 1077, http://dx.doi.org/10.21136/CMJ.2018.0085-17

Shparlinski IE, 2018, 'The Sato-Tate distribution in thin families of elliptic curves over high degree extensions of finite fields', International Journal of Number Theory, pp. 1 - 9, http://dx.doi.org/10.1142/S1793042119500246

Shparlinski IE, 2018, 'Trilinear forms with double Kloosterman sums', International Journal of Number Theory, vol. 14, pp. 2195 - 2203, http://dx.doi.org/10.1142/S1793042118501312

Shparlinski IE; Sutherland AV, 2018, 'On the Distribution of Atkin and Elkies Primes', Foundations of Computational Mathematics, vol. 14, pp. 285 - 297, http://dx.doi.org/10.1007/s10208-013-9181-9

Shparlinski IE; Winterhof A, 2018, 'Codes correcting restricted errors', Designs, Codes, and Cryptography, http://dx.doi.org/10.1007/s10623-018-0585-z

Shparlinski IE; Zhao L, 2018, 'Elliptic curves in isogeny classes', Journal of Number Theory, vol. 191, pp. 194 - 212, http://dx.doi.org/10.1016/j.jnt.2018.04.017

Shparlinski IE; Zumalacárregui A, 2018, 'Sums of inverses in thin sets of finite fields', Proceedings of the American Mathematical Society, vol. 146, pp. 1377 - 1388, http://dx.doi.org/10.1090/proc/13915

Simon M; Shkredov I; Shparlinski I, 2018, 'Multiplicative Energy of Shifted Subgroups and Bounds On Exponential Sums with Trinomials in Finite Fields', Canadian Journal of Mathematics, vol. 70, pp. 1319 - 1338, http://dx.doi.org/10.4153/CJM-2017-044-2

Banks WD; Shparlinski IE, 2017, 'On coincidences among quadratic fields generated by the shanks sequence', Quarterly Journal of Mathematics, vol. 68, pp. 465 - 484, http://dx.doi.org/10.1093/qmath/haw054

Bell J; Shparlinski IE, 2017, 'Power series approximations to Fekete polynomials', Journal of Approximation Theory, vol. 222, pp. 132 - 142, http://dx.doi.org/10.1016/j.jat.2017.07.002

Dietmann R; Elsholtz C; Shparlinski IE, 2017, 'Prescribing the binary digits of squarefree numbers and quadratic residues', Transactions of the American Mathematical Society, vol. 369, pp. 8369 - 8388, http://dx.doi.org/10.1090/tran/6903

Dubickas A; Sha M; Shparlinski IE, 2017, 'On distances in lattices from algebraic number fields', Moscow Mathematical Journal, vol. 17, pp. 239 - 268, http://dx.doi.org/10.17323/1609-4514-2017-17-2-239-268

Liu K; Shparlinski IE; Zhang T, 2017, 'Squares in Piatetski-Shapiro sequences', Acta Arithmetica, vol. 181, pp. 239 - 252, http://dx.doi.org/10.4064/aa8644-8-2017

Luca F; Sha M; Shparlinski IE, 2017, 'On two functions arising in the study of the euler and carmichael quotients', Colloquium Mathematicum, vol. 149, pp. 179 - 192, http://dx.doi.org/10.4064/cm6910-3-2017

Mans B; Sha M; Shparlinski IE; Sutantyo D, 2017, 'On Functional Graphs of Quadratic Polynomials', Experimental Mathematics, pp. 1 - 9, http://dx.doi.org/10.1080/10586458.2017.1391725

Pomerance C; Shparlinski IE, 2017, 'Connected components of the graph generated by power maps in prime finite fields', Connected components of the graph generated by power maps in prime finite fields, http://arxiv.org/abs/1703.09292v2

Shkredov ID; Shparlinski IE, 2017, 'ON SOME MULTIPLE CHARACTER SUMS', Mathematika, vol. 63, pp. 553 - 560, http://dx.doi.org/10.1112/S0025579317000055

Shparlinski IE, 2017, 'On the convex hull of the points on multivariate modular hyperbolas', Journal of Number Theory, vol. 171, pp. 71 - 78, http://dx.doi.org/10.1016/j.jnt.2016.07.011

Shparlinski IE; Sutherland AV, 2017, 'Finding elliptic curves with a subgroup of prescribed size', International Journal of Number Theory, vol. 13, pp. 133 - 152, http://dx.doi.org/10.1142/S1793042117500099

Shparlinski IE; Weingartner AJ, 2017, 'An explicit polynomial analogue of Romanoff's theorem', Finite Fields and their Applications, vol. 44, pp. 22 - 33, http://dx.doi.org/10.1016/j.ffa.2016.11.002

Shparlinski IE; Yau KH, 2017, 'Double exponential sums with exponential functions', International Journal of Number Theory, vol. 13, pp. 2531 - 2543, http://dx.doi.org/10.1142/S179304211750141X

Banks WD; Guo VZ; Shparlinski IE, 2016, 'Almost primes of the form ⌊p^c⌋', Indagationes Mathematicae, vol. 27, pp. 423 - 436, http://dx.doi.org/10.1016/j.indag.2015.10.002

Banks WD; Shparlinski IE, 2016, 'Fractional parts of Dedekind sums', International Journal of Number Theory, vol. 12, pp. 1137 - 1147, http://dx.doi.org/10.1142/S179304211650069X

Banks WD; Shparlinski IE, 2016, 'On Gauss sums and the evaluation of Stechkin's constant', Mathematics of Computation, vol. 85, pp. 2569 - 2581, http://dx.doi.org/10.1090/mcom3056

Banks WD; Shparlinski IE, 2016, 'On the number of distinct quadratic fields generated by the Shanks sequence', On the number of distinct quadratic fields generated by the Shanks sequence, http://arxiv.org/abs/1602.06473v1

Camburu OM; Ciolan EA; Luca F; Moree P; Shparlinski IE, 2016, 'Cyclotomic coefficients: Gaps and jumps', Journal of Number Theory, vol. 163, pp. 211 - 237, http://dx.doi.org/10.1016/j.jnt.2015.11.020

Chang MC; Shparlinski IE, 2016, 'On the density of integer points on generalised Markoff–Hurwitz and Dwork hypersurfaces', Mathematische Zeitschrift, vol. 282, pp. 935 - 954, http://dx.doi.org/10.1007/s00209-015-1571-z

Fité F; Shparlinski IE, 2016, 'On the singularity of the demjanenko matrix of quotients of fermat curves', Proceedings of the American Mathematical Society, vol. 144, pp. 55 - 63, http://dx.doi.org/10.1090/proc12717

Harman G; Shparlinski IE, 2016, 'Products of Small Integers in Residue Classes and Additive Properties of Fermat Quotients', International Mathematics Research Notices, vol. 2016, pp. 1424 - 1446, http://dx.doi.org/10.1093/imrn/rnv182

Heyman R; Shparlinski IE, 2016, 'Counting irreducible binomials over finite fields', Finite Fields and their Applications, vol. 38, pp. 1 - 12, http://dx.doi.org/10.1016/j.ffa.2015.12.001

Koh D; Shen CY; Shparlinski I, 2016, 'Averaging Operators Over Homogeneous Varieties Over Finite Fields', Journal of Geometric Analysis, vol. 26, pp. 1415 - 1441, http://dx.doi.org/10.1007/s12220-015-9595-5

Konyagin SV; Luca F; Mans B; Mathieson L; Sha M; Shparlinski IE, 2016, 'Functional graphs of polynomials over finite fields', Journal of Combinatorial Theory. Series B, vol. 116, pp. 87 - 122, http://dx.doi.org/10.1016/j.jctb.2015.07.003

Nguyen PQ; Shparlinski IE, 2016, 'Counting Co-cyclic lattices', SIAM Journal on Discrete Mathematics, vol. 30, pp. 1358 - 1370, http://dx.doi.org/10.1137/15M103950X

Rivat J; Shparlinski IE, 2016, 'Multiples of squares in short intervals', Functiones et Approximatio, Commentarii Mathematici, vol. 54, pp. 57 - 63, http://dx.doi.org/10.7169/facm/2016.54.1.5

Shparlinski IE, 2016, 'Groups generated by iterations of polynomials over finite fields', Proceedings of the Edinburgh Mathematical Society, vol. 59, pp. 235 - 245, http://dx.doi.org/10.1017/S0013091515000097

Shparlinski IE, 2016, 'Linear congruences with ratios', Proceedings of the American Mathematical Society, vol. 144, pp. 2837 - 2846, http://dx.doi.org/10.1090/proc/12949

Shparlinski IE, 2016, 'On bilinear exponential and character sums with reciprocals of polynomials', Mathematika, vol. 62, pp. 842 - 859, http://dx.doi.org/10.1112/S0025579316000036

Shparlinski IE, 2016, 'On small gaps between the elements of multiplicative subgroups of finite fields', Designs, Codes, and Cryptography, vol. 80, pp. 63 - 71, http://dx.doi.org/10.1007/s10623-015-0063-9

Shparlinski IE, 2016, 'On the additive energy of the distance set in finite fields', Finite Fields and their Applications, vol. 42, pp. 187 - 199, http://dx.doi.org/10.1016/j.ffa.2016.08.001

Shparlinski IE, 2016, 'Polynomial values in small subgroups of finite fields', Revista Matematica Iberoamericana, vol. 32, pp. 1127 - 1136, http://dx.doi.org/10.4171/RMI/909

Shparlinski IE, 2016, 'Ratios of Small Integers in Multiplicative Subgroups of Residue Rings', Experimental Mathematics, vol. 25, pp. 273 - 280, http://dx.doi.org/10.1080/10586458.2015.1091754

Shparlinski IE, 2016, 'SYSTEMS OF CONGRUENCES WITH PRODUCTS OF VARIABLES FROM SHORT INTERVALS', Bulletin of the Australian Mathematical Society, vol. 93, pp. 364 - 371, http://dx.doi.org/10.1017/S0004972715001240

Shparlinski IE; Yau KH, 2016, 'Bounds of double multiplicative character sums and gaps between residues of exponential functions', Journal of Number Theory, vol. 167, pp. 304 - 316, http://dx.doi.org/10.1016/j.jnt.2016.03.022

Shparlinski IE; Zhang T, 2016, 'Cancellations amongst Kloosterman sums', Acta Arithmetica, vol. 176, pp. 201 - 210, http://dx.doi.org/10.4064/aa8365-6-2016

Blackburn SR; Konyagin SV; Shparlinski IE, 2015, 'Counting additive decompositions of quadratic residues in finite fields', Functiones et Approximatio, Commentarii Mathematici, vol. 52, pp. 223 - 227, http://dx.doi.org/10.7169/facm/2015.52.2.3

Bourgain J; Konyagin SV; Shparlinski IE, 2015, 'Character sums and deterministic polynomial root finding in finite fields', Mathematics of Computation, vol. 84, pp. 2969 - 2977, http://dx.doi.org/10.1090/mcom/2946

Bretèche RDL; Sha M; Shparlinski IE; Voloch JF, 2015, 'The Sato-Tate Distribution in Thin Parametric Families of Elliptic Curves', Mathematische Zeitschrift, vol. 290, pp. 831 - 855, http://dx.doi.org/10.1007/s00209-018-2042-0

Chang MC; Shparlinski IE, 2015, 'On the density of integer points on generalised Markoff–Hurwitz and Dwork hypersurfaces', Mathematische Zeitschrift, http://dx.doi.org/10.1007/s00209-015-1571-z

Dubickas A; Sha M; Shparlinski I, 2015, 'Explicit form of Cassels' p-adic Embedding Theorem for Number Fields', Canadian Journal of Mathematics, vol. 67, pp. 1046 - 1064, http://dx.doi.org/10.4153/CJM-2015-021-2

Gómez-Pérez D; Shparlinski IE, 2015, 'Subgroups generated by rational functions in finite fields', Monatshefte fur Mathematik, vol. 176, pp. 241 - 253, http://dx.doi.org/10.1007/s00605-014-0697-0

Heyman R; Shparlinski IE, 2015, 'On the greatest common divisor of shifted sets', Journal of Number Theory, vol. 154, pp. 63 - 73, http://dx.doi.org/10.1016/j.jnt.2015.02.012

Koh D; Shen CY; Shparlinski I, 2015, 'Averaging Operators Over Homogeneous Varieties Over Finite Fields', Journal of Geometric Analysis, http://dx.doi.org/10.1007/s12220-015-9595-5

Konyagin SV; Shparlinski IE, 2015, 'Quadratic non-residues in short intervals', Proceedings of the American Mathematical Society, vol. 143, pp. 4261 - 4269, http://dx.doi.org/10.1090/S0002-9939-2015-12584-1

Kurlberg P; Luca F; Shparlinski IE, 2015, 'On the fixed points of the map x→x^x modulo a prime', Mathematical Research Letters, vol. 22, pp. 141 - 168, http://dx.doi.org/10.4310/MRL.2015.v22.n1.a8

Munsch M; Shparlinski IE, 2015, 'Congruences with intervals and subgroups modulo a prime', Michigan Mathematical Journal, vol. 64, pp. 655 - 672, http://dx.doi.org/10.1307/mmj/1441116662

Roche-Newton O; Shparlinski IE, 2015, 'Polynomial values in subfields and affine subspaces of finite fields', Quarterly Journal of Mathematics, vol. 66, pp. 693 - 706, http://dx.doi.org/10.1093/qmath/hau032

Sha M; Shparlinski IE, 2015, 'Lang-trotter and sato-tate distributions in single and double parametric families of elliptic curves', Acta Arithmetica, vol. 170, pp. 299 - 325, http://dx.doi.org/10.4064/aa170-4-1

Shparlinski I, 2015, 'Points on Varieties over Finite Fields in Small Boxes', Contemporary Mathematics, vol. 655, pp. 209 - 233, http://dx.doi.org/10.1090/conm/655/13235

Shparlinski IE, 2015, 'Cayley graphs generated by small degree polynomials over finite fields', SIAM Journal on Discrete Mathematics, vol. 29, pp. 376 - 381, http://dx.doi.org/10.1137/14095813X

Shparlinski IE, 2015, 'Close values of shifted modular inversions and the decisional modular inversion hidden number problem', Advances in Mathematics of Communications, vol. 9, pp. 169 - 176, http://dx.doi.org/10.3934/amc.2015.9.169

Shparlinski IE, 2015, 'Distribution of polynomial discriminants modulo a prime', Archiv der Mathematik, vol. 105, pp. 251 - 259, http://dx.doi.org/10.1007/s00013-015-0806-x

Shparlinski IE, 2015, 'On the product of small Elkies primes', Proceedings of the American Mathematical Society, vol. 143, pp. 1441 - 1448, http://dx.doi.org/10.1090/S0002-9939-2014-12345-8

Shparlinski IE, 2015, 'Small discriminants of complex multiplication fields of elliptic curves over finite fields', Czechoslovak Mathematical Journal, vol. 65, pp. 381 - 388, http://dx.doi.org/10.1007/s10587-015-0183-4

Shparlinski IE; Sutherland AV, 2015, 'On the distribution of Atkin and Elkies primes for reductions of elliptic curves on average', LMS Journal of Computation and Mathematics, vol. 18, pp. 308 - 322, http://dx.doi.org/10.1112/S1461157015000017

Von Zur Gathen J; Shparlinski IE, 2015, 'Circulant graphs and GCD and LCM of subsets', Information Processing Letters, vol. 115, pp. 134 - 138, http://dx.doi.org/10.1016/j.ipl.2014.07.014

Ahmadi O; Shparlinski IE, 2014, 'Exponential sums over points of elliptic curves', Journal of Number Theory, vol. 140, pp. 299 - 313, http://dx.doi.org/10.1016/j.jnt.2014.01.016

Blake IF; Luca F; Shparlinski IE, 2014, 'VSH and multiplicative modular relations between small primes with polynomial exponents', Applicable Algebra in Engineering, Communications and Computing, vol. 25, pp. 181 - 188, http://dx.doi.org/10.1007/s00200-014-0219-2

Chang MC; Cilleruelo J; Garaev MZ; Hernández J; Shparlinski IE; Zumalacárregui A, 2014, 'Points on curves in small boxes and applications', Michigan Mathematical Journal, vol. 63, pp. 503 - 534, http://dx.doi.org/10.1307/mmj/1409932631

Chang MC; Kerr B; Shparlinski IE; Zannier U, 2014, 'Elements of large order on varieties over prime finite fields', Journal de Theorie des Nombres de Bordeaux, vol. 26, pp. 579 - 593, http://dx.doi.org/10.5802/jtnb.880

Chang MC; Shparlinski IE, 2014, 'Double character sums over subgroups and intervals', Bulletin of the Australian Mathematical Society, vol. 90, pp. 376 - 390, http://dx.doi.org/10.1017/S0004972714000227

Chen Z; Shparlinski IE; Winterhof A, 2014, 'Covering sets for limited-magnitude errors', IEEE Transactions on Information Theory, vol. 60, pp. 5315 - 5321, http://dx.doi.org/10.1109/TIT.2014.2338078

Friedlander JB; Shparlinski IE, 2014, 'Enumeration of certain varieties over a finite field', Proceedings of the American Mathematical Society, vol. 142, pp. 2615 - 2623, http://dx.doi.org/10.1090/S0002-9939-2014-11999-X

Garcia-Morchon O; Rietman R; Shparlinski IE; Tolhuizen L, 2014, 'Interpolation and approximation of polynomials in finite fields over a short interval from noisy values', Experimental Mathematics, vol. 23, pp. 241 - 260, http://dx.doi.org/10.1080/10586458.2014.890918

Gómez-Pérez D; Ostafe A; Shparlinski I, 2014, 'Algebraic entropy, automorphisms and sparsity of algebraic dynamical systems and pseudorandom number generators', Mathematics of Computation, vol. 83, pp. 1535 - 1550, http://dx.doi.org/10.1090/S0025-5718-2013-02780-9

Gómez-Pérez D; Ostafe A; Shparlinski IE, 2014, 'On irreducible divisors of iterated polynomials', Revista Matematica Iberoamericana, vol. 30, pp. 1123 - 1134, http://dx.doi.org/10.4171/rmi/809

Ling S; Shparlinski I; Wang H, 2014, 'On the multidimensional distribution of the Naor-Reingold pseudo-random function', Mathematics of Computation, vol. 83, pp. 2429 - 2434, http://dx.doi.org/10.1090/S0025-5718-2014-02794-4

Luca F; Shparlinski IE, 2014, 'On the counting function of elliptic carmichael numbers', Canadian Mathematical Bulletin, vol. 57, pp. 105 - 112, http://dx.doi.org/10.4153/CMB-2012-037-4

Mans B; Shparlinski I, 2014, 'Random walks, bisections and gossiping in circulant graphs', Algorithmica, vol. 70, pp. 301 - 325, http://dx.doi.org/10.1007/s00453-013-9810-3

Munsch M; Shparlinski IE, 2014, 'Upper and Lower Bounds for Higher Moments of Theta Functions', Quarterly Journal of Mathematics, vol. 67, pp. 53 - 73, http://dx.doi.org/10.1093/qmath/hav039

Shparlinski IE, 2014, 'Distribution of exponential functions modulo a prime power', Journal of Number Theory, vol. 143, pp. 224 - 231, http://dx.doi.org/10.1016/j.jnt.2014.04.010

Shparlinski IE, 2014, 'Evasive properties of sparse graphs and some linear equations in primes', Theoretical Computer Science, vol. 547, pp. 117 - 121, http://dx.doi.org/10.1016/j.tcs.2014.06.005

Shparlinski IE, 2014, 'Multiple exponential and character sums with monomials', Mathematika, vol. 60, pp. 363 - 373, http://dx.doi.org/10.1112/S0025579314000084

Shparlinski IE, 2014, 'On solutions to some polynomial congruences in small boxes', Bulletin of the Australian Mathematical Society, vol. 89, pp. 300 - 307, http://dx.doi.org/10.1017/S0004972713000671

Shparlinski IE, 2014, 'On the distribution of points on the generalized markoff-hurwitz and dwork hypersurfaces', International Journal of Number Theory, vol. 10, pp. 151 - 160, http://dx.doi.org/10.1142/S1793042113500863

Shparlinski IE, 2014, 'Products with variables from low-dimensional affine spaces and shifted power identity testing in finite fields', Journal of Symbolic Computation, vol. 64, pp. 35 - 41, http://dx.doi.org/10.1016/j.jsc.2013.12.005

Shparlinski IE, 2014, 'Squarefree parts of discriminants of trinomials', Archiv der Mathematik, vol. 102, pp. 545 - 554, http://dx.doi.org/10.1007/s00013-014-0654-0

Shparlinski IE; Sutantyo D, 2014, 'Distribution of elliptic twin primes in isogeny and isomorphism classes', Journal of Number Theory, vol. 137, pp. 1 - 15, http://dx.doi.org/10.1016/j.jnt.2013.10.018

Shparlinski IE; Sutherland AV, 2014, 'On the Distribution of Atkin and Elkies Primes', Foundations of Computational Mathematics, pp. 1 - 13, http://dx.doi.org/10.1007/s10208-013-9181-9

Baker RC; Banks WD; Brüdern J; Shparlinski IE; Weingartner AJ, 2013, 'Piatetski-Shapiro sequences', Acta Arithmetica, vol. 157, pp. 37 - 68, http://dx.doi.org/10.4064/aa157-1-3

Borwein JM; Shparlinski I; Zudilin W, 2013, 'Number Theory and Related Fields: In Memory of Alf van der Poorten', Springer Proceedings in Mathematics and Statistics, vol. 43, http://dx.doi.org/10.1007/978-1-4614-6642-0

Bourgain J; Garaev MZ; Konyagin SV; Shparlinski IE, 2013, 'On congruences with products of variables from short intervals and applications', Proceedings of the Steklov Institute of Mathematics, vol. 280, pp. 61 - 90, http://dx.doi.org/10.1134/S0081543813010057

Cilleruelo J; Kumchev A; Luca F; Rué J; Shparlinski IE, 2013, 'On the fractional parts of aⁿ/n', Bulletin of the London Mathematical Society, vol. 45, pp. 249 - 256, http://dx.doi.org/10.1112/blms/bds084

Cilleruelo J; Shparlinski I, 2013, 'Concentration of points on curves in finite fields', Monatshefte fur Mathematik, vol. 171, pp. 315 - 327, http://dx.doi.org/10.1007/s00605-013-0498-x

Dietmann R; Elsholtz C; Shparlinski IE, 2013, 'On gaps between primitive roots in the hamming metric', Quarterly Journal of Mathematics, vol. 64, pp. 1043 - 1055, http://dx.doi.org/10.1093/qmath/has022

Dietmann R; Elsholtz C; Shparlinski IE, 2013, 'On gaps between quadratic non-residues in the Euclidean and Hamming metrics', Indagationes Mathematicae, vol. 24, pp. 930 - 938, http://dx.doi.org/10.1016/j.indag.2013.02.005

Farashahi RR; Fouque PA; Shparlinski IE; Tibouchi M; Voloch JF, 2013, 'Indifferentiable deterministic hashing to elliptic and hyperelliptic curves', Mathematics of Computation, vol. 82, pp. 491 - 512, http://dx.doi.org/10.1090/S0025-5718-2012-02606-8

Gutierrez J; Ibeas A; Gómez-Pérez D; Shparlinski IE, 2013, 'Predicting masked linear pseudorandom number generators over finite fields', Designs, Codes, and Cryptography, vol. 67, pp. 395 - 402, http://dx.doi.org/10.1007/s10623-012-9615-4

Harvey D; Shparlinski IE, 2013, 'Statistics of different reduction types of fermat curves', Experimental Mathematics, vol. 22, pp. 243 - 249, http://dx.doi.org/10.1080/10586458.2013.790201

Heyman R; Shparlinski IE, 2013, 'On the number of Eisenstein polynomials of bounded height', Applicable Algebra in Engineering, Communications and Computing, vol. 24, pp. 149 - 156, http://dx.doi.org/10.1007/s00200-013-0187-y

Kerr B; Shparlinski IE, 2013, 'On the distribution of values and zeros of polynomial systems over arbitrary sets', Journal of Number Theory, vol. 133, pp. 2863 - 2873, http://dx.doi.org/10.1016/j.jnt.2013.02.012

Konyagin SV; Luca F; Mans B; Mathieson L; Sha M; Shparlinski IE, 2013, 'Functional graphs of polynomials over finite fields', Journal of Combinatorial Theory. Series B, http://dx.doi.org/10.1016/j.jctb.2015.07.003

Shparlinski I, 2013, 'Erratum: Sum-product estimates and multiplicative orders ofΓ and Γ + Γ^-1 in finite fields (Bulletin of the Australian Mathematical Society)', Bulletin of the Australian Mathematical Society, vol. 87, pp. 527 - 528, http://dx.doi.org/10.1017/S0004972712001062

Shparlinski IE, 2013, 'Additive decompositions of subgroups of finite fields', SIAM Journal on Discrete Mathematics, vol. 27, pp. 1870 - 1879, http://dx.doi.org/10.1137/130924470

Shparlinski IE, 2013, 'Correcting noisy exponentiation black-boxes modulo a prime', Information Processing Letters, vol. 113, pp. 414 - 417, http://dx.doi.org/10.1016/j.ipl.2013.03.016

Shparlinski IE, 2013, 'Elliptic curves over finite fields: Number theoretic and cryptographic aspects', Fields Institute Communications, vol. 66, pp. 65 - 90, http://dx.doi.org/10.1007/978-1-4614-5389-5_4

Shparlinski IE, 2013, 'Evasive properties of sparse graphs and some linear equations in primes', Theoretical Computer Science, http://dx.doi.org/10.1016/j.tcs.2014.06.005

Shparlinski IE, 2013, 'On products of primes and almost primes in arithmetic progressions', Periodica Mathematica Hungarica, vol. 67, pp. 55 - 61, http://dx.doi.org/10.1007/s10998-013-2736-3

Shparlinski IE, 2013, 'On some exponential sums with exponential and rational functions', Rocky Mountain Journal of Mathematics, vol. 43, pp. 361 - 371, http://dx.doi.org/10.1216/RMJ-2013-43-1-361

Shparlinski IE, 2013, 'On the Lang-Trotter and Sato-Tate conjectures on average for polynomial families of elliptic curves', Michigan Mathematical Journal, vol. 62, pp. 491 - 505, http://dx.doi.org/10.1307/mmj/1378757885

Shparlinski IE, 2013, 'On the Sato-Tate conjecture on average for some families of elliptic curves', Forum Mathematicum, vol. 25, pp. 647 - 664, http://dx.doi.org/10.1515/FORM.2011.141

Shparlinski IE, 2013, 'On the average number of square-free values of polynomials', Canadian Mathematical Bulletin, vol. 56, pp. 844 - 849, http://dx.doi.org/10.4153/CMB-2012-021-8

Shparlinski IE, 2013, 'On vanishing Fermat quotients and a bound of the Ihara sum', Kodai Mathematical Journal, vol. 36, pp. 99 - 108, http://dx.doi.org/10.2996/kmj/1364562722

Shparlinski IE; Steiner W, 2013, 'On digit patterns in expansions of rational numbers with prime denominator', Quarterly Journal of Mathematics, vol. 64, pp. 1231 - 1238, http://dx.doi.org/10.1093/qmath/has027

Shparlinski IE; Winterhof A, 2013, 'Distribution of values of polynomial Fermat quotients', Finite Fields and their Applications, vol. 19, pp. 93 - 104, http://dx.doi.org/10.1016/j.ffa.2012.10.004

Von Zur Gathen J; Shparlinski IE, 2013, 'Generating safe primes', Journal of Mathematical Cryptology, vol. 7, pp. 333 - 365, http://dx.doi.org/10.1515/jmc-2013-5011

Ahmadi O; Luca F; Ostafe A; Shparlinski IE, 2012, 'On stable quadratic polynomials', Glasgow Mathematical Journal, vol. 54, pp. 359 - 369, http://dx.doi.org/10.1017/S001708951200002X

Balog A; Broughan KA; Shparlinski IE, 2012, 'Sum-Products Estimates with Several Sets and Applications', Integers, vol. 12, http://dx.doi.org/10.1515/integers-2012-0012

Banks WD; Friedlander JB; Garaev MZ; Shparlinski IE, 2012, 'Exponential and character sums with mersenne numbers', Journal of the Australian Mathematical Society, vol. 92, pp. 1 - 13, http://dx.doi.org/10.1017/S1446788712000109

Banks WD; Pappalardi F; Shparlinski IE, 2012, 'On group structures realized by elliptic curves over arbitrary finite fields', Experimental Mathematics, vol. 21, pp. 11 - 25, http://dx.doi.org/10.1080/10586458.2011.606075

Bourgain J; Garaev MZ; Konyagin SV; Shparlinski IE, 2012, 'On the hidden shifted power problem', SIAM Journal on Computing, vol. 41, pp. 1524 - 1557, http://dx.doi.org/10.1137/110850414

Bourgain J; Konyagin SV; Shparlinski IE, 2012, 'Distribution of elements of cosets of small subgroups and applications', International Mathematics Research Notices, vol. 2012, pp. 1968 - 2009, http://dx.doi.org/10.1093/imrn/rnr097

Cilleruelo J; Garaev MZ; Ostafe A; Shparlinski IE, 2012, 'On the concentration of points of polynomial maps and applications', Mathematische Zeitschrift, vol. 272, pp. 825 - 837, http://dx.doi.org/10.1007/s00209-011-0959-7

Cilleruelo J; Shparlinski IE; Zumalacárregui A, 2012, 'Isomorphism classes of elliptic curves over a finite field in some thin families', Mathematical Research Letters, vol. 19, pp. 335 - 343, http://dx.doi.org/10.4310/MRL.2012.v19.n2.a6

Cojocaru AC; Luca F; Shparlinski IE, 2012, 'Erratum: Pseudoprime reductions of elliptic curves (Mathematical Proceedings of the Cambridge Philosophical Society (2009) 146 (513-522))', Mathematical Proceedings of the Cambridge Philosophical Society, vol. 152, pp. 571, http://dx.doi.org/10.1017/S0305004111000399

Farashahi RR; Shparlinski IE, 2012, 'On group structures realized by elliptic curves over a fixed finite field', Experimental Mathematics, vol. 21, pp. 1 - 10, http://dx.doi.org/10.1080/10586458.2012.632754

Farashahi RR; Shparlinski IE, 2012, 'Pseudorandom bits from points on elliptic curves', IEEE Transactions on Information Theory, vol. 58, pp. 1242 - 1247, http://dx.doi.org/10.1109/TIT.2011.2170054

González JJA; Luca F; Pomerance C; Shparlinski IE, 2012, 'On numbers n dividing the nth term of a linear recurrence', Proceedings of the Edinburgh Mathematical Society, vol. 55, pp. 271 - 289, http://dx.doi.org/10.1017/S0013091510001355

Konyagin SV; Shparlinski IE, 2012, 'On the consecutive powers of a primitive root: Gaps and exponential sums', Mathematika, vol. 58, pp. 11 - 20, http://dx.doi.org/10.1112/S0025579311002117

Ling S; Shparlinski IE; Steinfeld R; Wang H, 2012, 'On the modular inversion hidden number problem', Journal of Symbolic Computation, vol. 47, pp. 358 - 367, http://dx.doi.org/10.1016/j.jsc.2011.09.002

Mans B; Shparlinski IE, 2012, 'Random walks and bisections in random circulant graphs', Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 7256 LNCS, pp. 542 - 555, http://dx.doi.org/10.1007/978-3-642-29344-3_46

Ostafe A; Shparlinski I, 2012, 'Degree growth, linear independence and periods of a class of rational dynamical systems', ARITHMETIC, GEOMETRY, CRYPTOGRAPHY AND CODING THEORY, vol. 574, pp. 131 - 143, http://dx.doi.org/10.1090/conm/574/11426

Ostafe A; Shparlinski IE, 2012, 'Exponential sums over points of elliptic curves with reciprocals of primes', Mathematika, vol. 58, pp. 21 - 33, http://dx.doi.org/10.1112/S0025579311001719

Ostafe A; Shparlinski IE, 2012, 'Multiplicative character sums and products of sparse integers in residue classes', Periodica Mathematica Hungarica, vol. 64, pp. 247 - 255, http://dx.doi.org/10.1007/s10998-012-6771-2

Ostafe A; Shparlinski IE, 2012, 'On the power generator and its multivariate analogue', Journal of Complexity, vol. 28, pp. 238 - 249, http://dx.doi.org/10.1016/j.jco.2011.10.010

Shparlinski I, 2012, 'Sum-product estimates and multiplicative orders of γ and γ+γ ^-1 in finite fields', Bulletin of the Australian Mathematical Society, vol. 85, pp. 505 - 508, http://dx.doi.org/10.1017/S0004972711002887

Shparlinski IE, 2012, 'Modular hyperbolas', Japanese Journal of Mathematics, vol. 7, pp. 235 - 294, http://dx.doi.org/10.1007/s11537-012-1140-8

Shparlinski IE, 2012, 'On the convex hull of solutions to polynomial congruences', Journal of Number Theory, vol. 132, pp. 254 - 257, http://dx.doi.org/10.1016/j.jnt.2011.06.016

Shparlinski IE, 2012, 'On the distribution of solutions to polynomial congruences', Archiv der Mathematik, vol. 99, pp. 345 - 351, http://dx.doi.org/10.1007/s00013-012-0436-5

Shparlinski IE, 2012, 'On the restricted divisor function in arithmetic progressions', Revista Matematica Iberoamericana, vol. 28, pp. 231 - 238, http://dx.doi.org/10.4171/rmi/675

Shparlinski IE, 2012, 'On the value set of fermat quotients', Proceedings of the American Mathematical Society, vol. 140, pp. 1199 - 1206, http://dx.doi.org/10.1090/S0002-9939-2011-11203-6

Shparlinski IE; Stange KE, 2012, 'Character sums with division polynomials', Canadian Mathematical Bulletin, vol. 55, pp. 850 - 857, http://dx.doi.org/10.4153/CMB-2011-126-x

Urroz JJ; Luca F; Shparlinski IE, 2012, 'On the number of isogeny classes of pairing-friendly elliptic curves and statistics of mnt curves', Mathematics of Computation, vol. 81, pp. 1093 - 1110, http://dx.doi.org/10.1090/S0025-5718-2011-02543-3

Balog A; Broughan KA; Shparlinski IE, 2011, 'On the number of solutions of exponential congruences', Acta Arithmetica, vol. 148, pp. 93 - 103, http://dx.doi.org/10.4064/aa148-1-7

Bibak K; Shparlinski IE, 2011, 'On Fully Split Lacunary Polynomials in Finite Fields', Bulletin of the Polish Academy of Sciences Mathematics, vol. 59, pp. 197 - 202, http://dx.doi.org/10.4064/ba59-3-1

Blackburn SR; Ostafe A; Shparlinski IE, 2011, 'On the Distribution of the Subset Sum Pseudorandom Number Generator on Elliptic Curves', On the Distribution of the Subset Sum Pseudorandom Number Generator on Elliptic Curves, http://arxiv.org/abs/1102.1053v1

Blackburn SR; Ostafe A; Shparlinski IE, 2011, 'On the Distribution of the Subset Sum Pseudorandom Number Generator on Elliptic Curves', CoRR, vol. abs/1102.1053

Fouvry E; Luca F; Pappalardi F; Shparlinski IE, 2011, 'Counting dihedral and quaternionic extensions', Transactions of the American Mathematical Society, vol. 363, pp. 3233 - 3253, http://dx.doi.org/10.1090/S0002-9947-2011-05233-5

Fouvry E; Shparlinski IE, 2011, 'On a ternary quadratic form over primes', Acta Arithmetica, vol. 150, pp. 285 - 314, http://dx.doi.org/10.4064/aa150-3-5

Fouvry E; Shparlinski IE, 2011, 'Smooth shifted monomial products', Publicationes Mathematicae, vol. 79, pp. 423 - 432, http://dx.doi.org/10.5486/PMD.2011.5089

Křížek M; Luca F; Shparlinski IE; Somer L, 2011, 'On the complexity of testing elite primes', Journal of Integer Sequences, vol. 14, pp. 1 - 5

Luca F; Shparlinski IE, 2011, 'On the g-Ary expansions of middle binomial coefficients and catalan numbers', Rocky Mountain Journal of Mathematics, vol. 41, pp. 1291 - 1301, http://dx.doi.org/10.1216/RMJ-2011-41-4-1291

Ostafe A; Shparlinski IE, 2011, 'On the waring problem with Dickson polynomials in finite fields', Proceedings of the American Mathematical Society, vol. 139, pp. 3815 - 3820, http://dx.doi.org/10.1090/S0002-9939-2011-10843-8

Ostafe A; Shparlinski IE, 2011, 'Pseudorandomness and dynamics of fermat quotients*', SIAM Journal on Discrete Mathematics, vol. 25, pp. 50 - 71, http://dx.doi.org/10.1137/100798466

Ostafe A; Shparlinski IE, 2011, 'Twisted exponential sums over points of elliptic curves', Acta Arithmetica, vol. 148, pp. 77 - 92, http://dx.doi.org/10.4064/aa148-1-6

Ostafe A; Shparlinski IE; Winterhof A, 2011, 'Multiplicative character sums of a class of nonlinear recurrence vector sequences', International Journal of Number Theory, vol. 7, pp. 1557 - 1571, http://dx.doi.org/10.1142/S1793042111004484

Shparlinski IE, 2011, 'Bounds of multiplicative character sums with Fermat quotients of primes', Bulletin of the Australian Mathematical Society, vol. 83, pp. 456 - 462, http://dx.doi.org/10.1017/S000497271000198X

Shparlinski IE, 2011, 'Character sums with fermat quotients', Quarterly Journal of Mathematics, vol. 62, pp. 1031 - 1043, http://dx.doi.org/10.1093/qmath/haq028

Shparlinski IE, 2011, 'Exponential sums with consecutive modular roots of an integer', Quarterly Journal of Mathematics, vol. 62, pp. 207 - 213, http://dx.doi.org/10.1093/qmath/hap023

Shparlinski IE, 2011, 'Fermat quotients: Exponential sums, value set and primitive roots', Bulletin of the London Mathematical Society, vol. 43, pp. 1228 - 1238, http://dx.doi.org/10.1112/blms/bdr058

Shparlinski IE, 2011, 'On small solutions to quadratic congruences', Journal of Number Theory, vol. 131, pp. 1105 - 1111, http://dx.doi.org/10.1016/j.jnt.2010.12.002

Shparlinski IE, 2011, 'On the average distribution of pseudorandom numbers generated by nonlinear permutations', Mathematics of Computation, vol. 80, pp. 1053 - 1061, http://dx.doi.org/10.1090/S0025-5718-2010-02408-1

Shparlinski IE, 2011, 'On the distribution of irreducible trinomials', Canadian Mathematical Bulletin, vol. 54, pp. 748 - 756, http://dx.doi.org/10.4153/CMB-2011-053-0

Ahmadi O; Shparlinski I, 2010, 'Bilinear character sums and sum-product problems on elliptic curves', Proceedings of the Edinburgh Mathematical Society, vol. 53, pp. 1 - 12, http://dx.doi.org/10.1017/S0013091508000771

Ahmadi O; Shparlinski IE, 2010, 'On the distribution of the number of points on algebraic curves in extensions of finite fields', Mathematical Research Letters, vol. 17, pp. 689 - 699, http://dx.doi.org/10.4310/MRL.2010.v17.n4.a9

Ahmadi O; Shparlinski IE; Voloch JF, 2010, 'Multiplicative order of gauss periods', International Journal of Number Theory, vol. 6, pp. 877 - 882, http://dx.doi.org/10.1142/S1793042110003290

Banks WD; Shparlinski IE, 2010, 'Sums with convolutions of Dirichlet characters', Manuscripta Mathematica, vol. 133, pp. 105 - 114, http://dx.doi.org/10.1007/s00229-010-0364-2

Bourgain J; Ford K; Konyagin SV; Shparlinski IE, 2010, 'On the divisibility of Fermat quotients', Michigan Mathematical Journal, vol. 59, pp. 313 - 328, http://dx.doi.org/10.1307/mmj/1281531459

Broughan KA; Luca F; Shparlinski IE, 2010, 'Some Divisibility Properties of Binomial Coefficients and the Converse of Wolstenholme's Theorem', Integers, vol. 10, http://dx.doi.org/10.1515/integ.2010.041

Chan TH; Shparlinski IE, 2010, 'On the concentration of points on modular hyperbolas and exponential curves', Acta Arithmetica, vol. 142, pp. 59 - 66, http://dx.doi.org/10.4064/aa142-1-5

Chan TH; Shparlinski IE, 2010, 'Visible Points on Modular Exponential Curves', Bulletin of the Polish Academy of Sciences Mathematics, vol. 58, pp. 17 - 22, http://dx.doi.org/10.4064/ba58-1-2

Cilleruelo J; Luca F; Quirós A; Shparlinski IE, 2010, 'On squares in polynomial products', Monatshefte fur Mathematik, vol. 159, pp. 215 - 223, http://dx.doi.org/10.1007/s00605-008-0066-y

Farashahi RR; Shparlinski IE, 2010, 'On pseudopoints of algebraic curves', Archiv der Mathematik, vol. 95, pp. 529 - 537, http://dx.doi.org/10.1007/s00013-010-0200-7

Ferguson R; Hoffman C; Luca F; Ostafe A; Shparlinski IE, 2010, 'Some additive combinatorics problems in matrix rings', Revista Matematica Complutense, vol. 23, pp. 501 - 513, http://dx.doi.org/10.1007/s13163-010-0029-4

Ford K; Khan MR; Shparlinski IE, 2010, 'Geometric properties of points on modular hyperbolas', Proceedings of the American Mathematical Society, vol. 138, pp. 4177 - 4185, http://dx.doi.org/10.1090/S0002-9939-2010-10561-0

Friedlander JB; Gong K; Shparlinskii IE, 2010, 'Character sums over shifted primes', Mathematical Notes, vol. 88, pp. 585 - 598, http://dx.doi.org/10.1134/S0001434610090312

Glebsky L; Shparlinski IE, 2010, 'Short cycles in repeated exponentiation modulo a prime', Designs, Codes, and Cryptography, vol. 56, pp. 35 - 42, http://dx.doi.org/10.1007/s10623-009-9339-2

Gutierrez J; Shparlinski IE, 2010, 'Expansion of orbits of some dynamical systems over finite fields', Bulletin of the Australian Mathematical Society, vol. 82, pp. 232 - 239, http://dx.doi.org/10.1017/S0004972709001270

Iosevich A; Shparlinski IE; Xiong M, 2010, 'SETS WITH INTEGRAL DISTANCES IN FINITE FIELDS', TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, vol. 362, pp. 2189 - 2204, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000275819200020&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Iosevich A; Shparlinski IE; Xiong M, 2010, 'Sets with integral distances in finite fields', Transactions of the American Mathematical Society, vol. 362, pp. 2189 - 2204, http://dx.doi.org/10.1090/S0002-9947-09-05004-1

Karabina K; Menezes A; Pomerance C; Shparlinski IE, 2010, 'On the asymptotic effectiveness of Weil descent attacks', Journal of Mathematical Cryptology, vol. 4, pp. 175 - 191, http://dx.doi.org/10.1515/JMC.2010.007

Konyagin SV; Pomerance C; Shparlinski IE, 2010, 'On the distribution of pseudopowers', Canadian Journal of Mathematics, vol. 62, pp. 582 - 594, http://dx.doi.org/10.4153/CJM-2010-020-4

Konyagin SV; Shparlinski IE, 2010, 'On the Convex Hull of the Points on Modular Hyperbolas', On the Convex Hull of the Points on Modular Hyperbolas, http://arxiv.org/abs/1012.1444v2

Loiperdinger SS; Shparlinski IE, 2010, 'ON THE DISTRIBUTION OF THE EULER FUNCTION OF SHIFTED SMOOTH NUMBERS', COLLOQUIUM MATHEMATICUM, vol. 120, pp. 139 - 148, http://dx.doi.org/10.4064/cm120-1-10

Luca F; Shparlinski IE, 2010, 'On the g-Ary Expansions of Apéry, Motzkin, Schröder and Other Combinatorial Numbers', Annals of Combinatorics, vol. 14, pp. 507 - 524, http://dx.doi.org/10.1007/s00026-011-0074-9

Ostafe A; Pelican E; Shparlinski IE, 2010, 'On pseudorandom numbers from multivariate polynomial systems', Finite Fields and their Applications, vol. 16, pp. 320 - 328, http://dx.doi.org/10.1016/j.ffa.2010.05.002

Ostafe A; Shparlinski IE, 2010, 'On the degree growth in some polynomial dynamical systems and nonlinear pseudorandom number generators', Mathematics of Computation, vol. 79, pp. 501 - 511, http://dx.doi.org/10.1090/S0025-5718-09-02271-6

Ostafe A; Shparlinski IE, 2010, 'On the length of critical orbits of stable quadratic polynomials', Proceedings of the American Mathematical Society, vol. 138, pp. 2653 - 2656, http://dx.doi.org/10.1090/S0002-9939-10-10404-3

Ostafe A; Shparlinski IE, 2010, 'Pseudorandom numbers and hash functions from iterations of multivariate polynomials', Cryptography and Communications, vol. 2, pp. 49 - 67, http://dx.doi.org/10.1007/s12095-009-0016-0

Ostafe A; Shparlinski IE; Winterhof A, 2010, 'On the generalized joint linear complexity profile of a class of nonlinear pseudorandom multisequences', Advances in Mathematics of Communications, vol. 4, pp. 369 - 379, http://dx.doi.org/10.3934/amc.2010.4.369

Pomerance C; Shparlinski IE, 2010, 'Rank statistics for a family of elliptic curves over a function field', Pure and Applied Mathematics Quarterly, vol. 6, pp. 21 - 40, http://dx.doi.org/10.4310/PAMQ.2010.v6.n1.a2

Rezaeian Farashahi R; Shparlinski IE, 2010, 'On the number of distinct elliptic curves in some families', Designs, Codes, and Cryptography, vol. 54, pp. 83 - 99, http://dx.doi.org/10.1007/s10623-009-9310-2

Shparlinski IE, 2010, 'Numbers at work and play', Notices of the American Mathematical Society, vol. 57, pp. 334 - 342

Shparlinski IE, 2010, 'On point sets in vector spaces over finite fields that determine only acute angle triangles', Bulletin of the Australian Mathematical Society, vol. 81, pp. 114 - 120, http://dx.doi.org/10.1017/S0004972709000719

Shparlinski IE, 2010, 'On quadratic fields generated by discriminants of irreducible trinomials', Proceedings of the American Mathematical Society, vol. 138, pp. 125 - 132, http://dx.doi.org/10.1090/S0002-9939-09-10074-6

Shparlinski IE, 2010, 'On the size of the Gelfond exponent', Journal of Number Theory, vol. 130, pp. 1056 - 1060, http://dx.doi.org/10.1016/j.jnt.2009.09.005

Shparlinski IE, 2010, 'Some counting questions for matrices with restricted entries', Linear Algebra and Its Applications, vol. 432, pp. 155 - 160, http://dx.doi.org/10.1016/j.laa.2009.07.036

Shparlinski IE, 2010, 'Tate-shafarevich groups and frobenius fields of reductions of elliptic curves', Quarterly Journal of Mathematics, vol. 61, pp. 255 - 263, http://dx.doi.org/10.1093/qmath/hap001

Shparlinski IE; Winterhof A, 2010, 'Partitions into two Lehmer numbers', Monatshefte fur Mathematik, vol. 160, pp. 429 - 441, http://dx.doi.org/10.1007/s00605-009-0130-2

von zur Gathen J; Mignotte M; Shparlinski IE, 2010, 'Approximate polynomial gcd: Small degree and small height perturbations', Journal of Symbolic Computation, vol. 45, pp. 879 - 886, http://dx.doi.org/10.1016/j.jsc.2010.04.001

Фридландер ДБ; Friedlander JB; Гонг K; Gong K; Шпарлинский ИЕ; Shparlinski IE, 2010, 'Суммы значений характеров на сдвинутых простых числах', Matematicheskie Zametki, vol. 88, pp. 605 - 619, http://dx.doi.org/10.4213/mzm8692

Abercrombie AG; Banks WD; Shparlinski IE, 2009, 'Arithmetic functions on Beatty sequences', Acta Arithmetica, vol. 136, pp. 81 - 89, http://dx.doi.org/10.4064/aa136-1-6

Ahmadi O; Alon N; Blake IF; Shparlinski IE, 2009, 'Graphs with integral spectrum', Linear Algebra and Its Applications, vol. 430, pp. 547 - 552, http://dx.doi.org/10.1016/j.laa.2008.08.020

Balasuriya S; Shparlinski IE; Sutantyo D, 2009, 'Multiplicative character sums with the Euler function', Studia Scientiarum Mathematicarum Hungarica, vol. 46, pp. 223 - 229, http://dx.doi.org/10.1556/SScMath.46.2009.2.1087

Balasuriya S; Winterhof A; Shparlinski IE, 2009, 'An average bound for character sums with some counter-dependent recurrence sequences', Rocky Mountain Journal of Mathematics, vol. 39, pp. 1403 - 1409, http://dx.doi.org/10.1216/RMJ-2009-39-5-1403

Banks WD; Garaev MZ; Luca F; Shparlinski IE, 2009, 'Uniform Distribution of Fractional Parts Related to Pseudoprimes', Canadian Journal of Mathematics, vol. 61, pp. 481 - 502, http://dx.doi.org/10.4153/CJM-2009-025-2

Banks WD; Shparlinski IE, 2009, 'Multiplicative character sums with twice-differentiable functions', Quarterly Journal of Mathematics, vol. 60, pp. 401 - 411, http://dx.doi.org/10.1093/qmath/han023

Banks WD; Shparlinski IE, 2009, 'Prime numbers with beatty sequences', Colloquium Mathematicum, vol. 115, pp. 147 - 157, http://dx.doi.org/10.4064/cm115-2-1

Banks WD; Shparlinski IE, 2009, 'Sato-Tate, cyclicity, and divisibility statistics on average for elliptic curves of small height', Israel Journal of Mathematics, vol. 173, pp. 253 - 277, http://dx.doi.org/10.1007/s11856-009-0091-0

Bourgain J; Konyagin SV; Pomerance C; Shparlinski IE, 2009, 'On the smallest pseudopower', Acta Arithmetica, vol. 140, pp. 43 - 55, http://dx.doi.org/10.4064/aa140-1-3

Bourgain J; Konyagin SV; Shparlinski IE, 2009, 'Erratum: Product sets of rationals, multiplicative translates of subgroups in residue rings and fixed points of the discrete logarithm (International Mathematics Research Notices)', International Mathematics Research Notices, vol. 2009, pp. 3146 - 3147, http://dx.doi.org/10.1093/imrn/rnp041

Cojocaru AC; Luca F; Shparlinski IE, 2009, 'Pseudoprime reductions of elliptic curves', Mathematical Proceedings of the Cambridge Philosophical Society, vol. 146, pp. 513 - 522, http://dx.doi.org/10.1017/S0305004108001758

Cojocaru AC; Shparlinski IE, 2009, 'On the embedding degree of reductions of an elliptic curve', Information Processing Letters, vol. 109, pp. 652 - 654, http://dx.doi.org/10.1016/j.ipl.2009.02.018

Farashahi RR; Shparlinski IE; Voloch JF, 2009, 'On hashing into elliptic curves', Journal of Mathematical Cryptology, vol. 3, pp. 353 - 360, http://dx.doi.org/10.1515/JMC.2009.022

Ford K; Luca F; Shparlinski IE, 2009, 'On the largest prime factor of the mersenne numbers', Bulletin of the Australian Mathematical Society, vol. 79, pp. 455 - 463, http://dx.doi.org/10.1017/S0004972709000033

Friedlander JB; Shparlinski IE, 2009, 'Elliptic twin prime conjecture', Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 5557 LNCS, pp. 77 - 81, http://dx.doi.org/10.1007/978-3-642-01877-0_8

Friedlander JB; Shparlinski IE, 2009, 'On the density of some special primes', Journal of Mathematical Cryptology, vol. 3, pp. 265 - 271, http://dx.doi.org/10.1515/JMC.2009.016

Igor S, 2009, 'Some special character sums over elliptic curves', Boletin de la Sociedad Matematica Mexicana, vol. 15, pp. 37 - 40

Katz NM; Shparlinski IE; Xiong M, 2009, 'On character sums with distances on the upper half plane over a finite field', Finite Fields and their Applications, vol. 15, pp. 738 - 747, http://dx.doi.org/10.1016/j.ffa.2009.08.002

Luca F; Shparlinski IE, 2009, 'On quadratic fields generated by the Shanks sequence', Proceedings of the Edinburgh Mathematical Society, vol. 52, pp. 719 - 729, http://dx.doi.org/10.1017/S001309150700123X

Pomerance C; Shparlinski IE, 2009, 'On Pseudosquares and Pseudopowers', COMBINATORIAL NUMBER THEORY, pp. 171 - +, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000269082400013&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Shparlinski IE, 2009, 'Bilinear sums with exponential functions', Proceedings of the American Mathematical Society, vol. 137, pp. 2217 - 2224, http://dx.doi.org/10.1090/S0002-9939-09-09882-7

Shparlinski IE, 2009, 'EXPONENTS OF MODULAR REDUCTIONS OF FAMILIES OF ELLIPTIC CURVES', REVISTA DE LA UNION MATEMATICA ARGENTINA, vol. 50, pp. 69 - 74, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000268682800008&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Shparlinski IE, 2009, 'Exponential Sums with Farey Fractions', Bulletin of the Polish Academy of Sciences Mathematics, vol. 57, pp. 101 - 107, http://dx.doi.org/10.4064/ba57-2-2

Shparlinski IE, 2009, 'On a generalisation of a Lehmer problem', Mathematische Zeitschrift, vol. 263, pp. 619 - 631, http://dx.doi.org/10.1007/s00209-008-0434-2

Shparlinski IE, 2009, 'On some weighted average values of l-functions', Bulletin of the Australian Mathematical Society, vol. 79, pp. 183 - 186, http://dx.doi.org/10.1017/S0004972708001020

Shparlinski IE, 2009, 'On the distribution of arguments of gauss sums', Kodai Mathematical Journal, vol. 32, pp. 172 - 177, http://dx.doi.org/10.2996/kmj/1238594554

Shparlinski IE, 2009, 'On the distribution of orbits of PGL2(q) in Fqn and the Klapper conjecture', SIAM Journal on Discrete Mathematics, vol. 23, pp. 2093 - 2099, http://dx.doi.org/10.1137/090770746

Shparlinski IE, 2009, 'On the distribution of solutions to linear equations', Glasnik Matematicki, vol. 44, pp. 7 - 10, http://dx.doi.org/10.3336/gm.44.1.02

Shparlinski IE, 2009, 'On the values of Kloosterman sums', IEEE Transactions on Information Theory, vol. 55, pp. 2599 - 2601, http://dx.doi.org/10.1109/TIT.2009.2018320

Von Zur Gathen J; Shparlinski IE, 2009, 'Subset sum pseudorandom numbers: Fast generation and distribution', Journal of Mathematical Cryptology, vol. 3, pp. 149 - 163, http://dx.doi.org/10.1515/JMC.2009.007

Balasuriya S; Banks WD; Shparlinski IE, 2008, 'Congruences and exponential sums with the sum of aliquot divisors function', International Journal of Number Theory, vol. 4, pp. 903 - 909, http://dx.doi.org/10.1142/S179304210800178X

Banks WD; Garaev MZ; Heath-Brown DR; Shparlinski IE, 2008, 'Density of non-residues in Burgess-type intervals and applications', Bulletin of the London Mathematical Society, vol. 40, pp. 88 - 96, http://dx.doi.org/10.1112/blms/bdm111

Blackburn SR; Shparlinski IE, 2008, 'On the average energy of circulant graphs', Linear Algebra and Its Applications, vol. 428, pp. 1956 - 1963, http://dx.doi.org/10.1016/j.laa.2007.11.003

Bourgain J; Konyagin SV; Shparlinski IE, 2008, 'Product sets of rationals, multiplicative translates of subgroups in residue rings, and fixed points of the discrete logarithm', International Mathematics Research Notices, vol. 2008, http://dx.doi.org/10.1093/imrn/rnn090

Bourgain J; Shparlinski IE, 2008, 'Distribution of consecutive modular roots of an integer', Acta Arithmetica, vol. 134, pp. 83 - 91, http://dx.doi.org/10.4064/aa134-1-6

Cojocaru AC; Shparlinski IE, 2008, 'Distribution of farey fractions in residue classes and lang-trotter conjectures on average', Proceedings of the American Mathematical Society, vol. 136, pp. 1977 - 1986, http://dx.doi.org/10.1090/S0002-9939-08-09324-6

Ford K; Shparlinski I, 2008, 'On curves over finite fields with Jacobians of small exponent', International Journal of Number Theory, vol. 4, pp. 819 - 826, http://dx.doi.org/10.1142/S1793042108001687

Friedlander JB; Kurlberg P; Shparlinski IE, 2008, 'PRODUCTS IN RESIDUE CLASSES', MATHEMATICAL RESEARCH LETTERS, vol. 15, pp. 1133 - 1147, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000262382600023&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Friedlander JB; Kurlberg P; Shparlinski IE, 2008, 'Products in residue classes', Mathematical Research Letters, vol. 15, pp. 1133 - 1147, http://dx.doi.org/10.4310/mrl.2008.v15.n6.a6

Friedlander JB; Shparlinski IE, 2008, 'Erratum: Least totient in a residue class (Bulletin of the London Mathematical Society (2007) 39 (425-432))', Bulletin of the London Mathematical Society, vol. 40, pp. 532, http://dx.doi.org/10.1112/blms/bdn037

Graham SW; Shparlinski IE, 2008, 'On RSA moduli with almost half of the bits prescribed', Discrete Applied Mathematics, vol. 156, pp. 3150 - 3154, http://dx.doi.org/10.1016/j.dam.2007.12.012

Khan MR; Shparlinski IE; Yankov CL, 2008, 'On the convex closure of the graph of modular inversions', Experimental Mathematics, vol. 17, pp. 91 - 104, http://dx.doi.org/10.1080/10586458.2008.10129021

Kohnen W; Lau YK; Shparlinski IE, 2008, 'On the number of sign changes of hecke eigenvalues of newforms', Journal of the Australian Mathematical Society, vol. 85, pp. 87 - 94, http://dx.doi.org/10.1017/S1446788708000323

Luca F; Shparlinski IE, 2008, 'Arithmetic properties of Apéry numbers', Journal of the London Mathematical Society, vol. 78, pp. 545 - 562, http://dx.doi.org/10.1112/jlms/jdn031

Luca F; Shparlinski IE, 2008, 'On quadratic fields generated by polynomials', Archiv der Mathematik, vol. 91, pp. 399 - 408, http://dx.doi.org/10.1007/s00013-008-2656-2

Luca F; Shparlinski IE, 2008, 'On the values of the divisor function', Monatshefte fur Mathematik, vol. 154, pp. 59 - 69, http://dx.doi.org/10.1007/s00605-007-0511-3

Luca F; Shparlinski IE; Thangadurai R, 2008, 'Quadratic non-residues versus primitive roots modulo p', Journal of the Ramanujan Mathematical Society, vol. 23, pp. 97 - 104

Naccache D; Shparlinski IE, 2008, 'Divisibility, Smoothness and Cryptographic Applications', Divisibility, Smoothness and Cryptographic Applications, http://arxiv.org/abs/0810.2067v3

Shparlinski I, 2008, 'Bilinear character sums over elliptic curves', Finite Fields and their Applications, vol. 14, pp. 132 - 141, http://dx.doi.org/10.1016/j.ffa.2006.12.005

Shparlinski I, 2008, 'On the elliptic curve analogue of the sum-product problem', Finite Fields and their Applications, vol. 14, pp. 721 - 726, http://dx.doi.org/10.1016/j.ffa.2007.12.002

Shparlinski I, 2008, 'On the exponential sum-product problem', Indagationes Mathematicae, vol. 19, pp. 325 - 331, http://dx.doi.org/10.1016/S0019-3577(08)80006-7

Shparlinski I, 2008, 'On the size of the Jacobians of curves over finite fields', Bulletin of the Brazilian Mathematical Society, vol. 39, pp. 587 - 595, http://dx.doi.org/10.1007/s00574-008-0006-4

Shparlinski IE, 2008, 'Approximation by several rationals', Bulletin of the Australian Mathematical Society, vol. 77, pp. 325 - 329, http://dx.doi.org/10.1017/S0004972708000373

Shparlinski IE, 2008, 'Arithmetic and geometric progressions in product sets over finite fields', Bulletin of the Australian Mathematical Society, vol. 78, pp. 357 - 364, http://dx.doi.org/10.1017/S0004972708000695

Shparlinski IE, 2008, 'Distribution of modular inverses and multiples of small integers and the Sato-Tate conjecture on average', Michigan Mathematical Journal, vol. 56, pp. 99 - 111, http://dx.doi.org/10.1307/mmj/1213972400

Shparlinski IE, 2008, 'Exponential sums and prime divisors of sparse integers', Periodica Mathematica Hungarica, vol. 57, pp. 93 - 99, http://dx.doi.org/10.1007/s10998-008-7093-3

Shparlinski IE, 2008, 'Infinite hilbert class field towers over cyclotomic fields', Glasgow Mathematical Journal, vol. 50, pp. 27 - 32, http://dx.doi.org/10.1017/S0017089507003977

Shparlinski IE, 2008, 'On a Generalised Lehmer Problem for Arbitrary Powers', On a Generalised Lehmer Problem for Arbitrary Powers, http://arxiv.org/abs/0803.3487v2

Shparlinski IE, 2008, 'On the Euler Function on Differences Between the Coordinates of Points on Modular Hyperbolas', Bulletin of the Polish Academy of Sciences Mathematics, vol. 56, pp. 1 - 7, http://dx.doi.org/10.4064/ba56-1-1

Shparlinski IE, 2008, 'On the distribution of Kloosterman sums', PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, vol. 136, pp. 419 - 425, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000251536800006&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Shparlinski IE, 2008, 'On the distribution of kloosterman sums', Proceedings of the American Mathematical Society, vol. 136, pp. 419 - 425, http://dx.doi.org/10.1090/S0002-9939-07-08943-5

Shparlinski IE, 2008, 'On the solvability of bilinear equations in finite fields', Glasgow Mathematical Journal, vol. 50, pp. 523 - 529, http://dx.doi.org/10.1017/S0017089508004382

Shparlinski IE, 2008, 'Pseudorandom graphs from elliptic curves', Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4957 LNCS, pp. 284 - 292, http://dx.doi.org/10.1007/978-3-540-78773-0_25

Shparlinski IE; Voloch JF, 2008, 'Average distribution of prime ideals in families of number fields', Bulletin of the Brazilian Mathematical Society, vol. 39, pp. 417 - 425, http://dx.doi.org/10.1007/s00574-008-0014-4

Shparlinski IE; Winterhof A, 2008, 'On the number of distances between the coordinates of points on modular hyperbolas', Journal of Number Theory, vol. 128, pp. 1224 - 1230, http://dx.doi.org/10.1016/j.jnt.2007.04.016

Shparlinski IE; Winterhof A, 2008, 'Visible points on multidimensional modular hyperbolas', Journal of Number Theory, vol. 128, pp. 2695 - 2703, http://dx.doi.org/10.1016/j.jnt.2008.02.011

Van Dam W; Shparlinski IE, 2008, 'Classical and quantum algorithms for exponential congruences', Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 5106 LNCS, pp. 1 - 10, http://dx.doi.org/10.1007/978-3-540-89304-2_1

Von Zur Gathen J; Shparlinski IE, 2008, 'Approximate polynomial gcd: Small degree and small height perturbations', Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4957 LNCS, pp. 276 - 283, http://dx.doi.org/10.1007/978-3-540-78773-0_24

Ahmadi O; Shparlinski IE, 2007, 'Distribution of matrices with restricted entries over finite fields', Indagationes Mathematicae, vol. 18, pp. 327 - 337, http://dx.doi.org/10.1016/S0019-3577(07)00013-4

Ahmadi O; Shparlinski IE, 2007, 'Geometric progressions in sumsets over finite fields', Monatshefte fur Mathematik, vol. 152, pp. 177 - 185, http://dx.doi.org/10.1007/s00605-007-0471-7

Balasuriya S; Luca F; Shparlinski IE, 2007, 'Prime Divisors Of Some Recurrence Sequence', Periodica Mathematica Hungarica, vol. 54, pp. 215 - 227, http://dx.doi.org/10.1007/s-10998-007-2215-z

Balasuriya S; Shparlinski IE, 2007, 'Character sums with subsequence sums', Periodica Mathematica Hungarica, vol. 55, pp. 215 - 221, http://dx.doi.org/10.1007/s10998-007-4215-4

Banks WD; Luca F; Shparlinski IE, 2007, 'Estimates for Wieferich numbers', Ramanujan Journal, vol. 14, pp. 361 - 378, http://dx.doi.org/10.1007/s11139-007-9030-z

Banks WD; Luca F; Shparlinski IE, 2007, 'On rough and smooth neighbours', REVISTA MATEMATICA COMPLUTENSE, vol. 20, pp. 109 - 118, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000254910400002&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Banks WD; Shparlinski IE, 2007, 'On values taken by the largest prime factor of shifted primes', Journal of the Australian Mathematical Society, vol. 82, pp. 133 - 147, http://dx.doi.org/10.1017/s1446788700017511

Banks WD; Shparlinski IE, 2007, 'Prime divisors in Beatty sequences', Journal of Number Theory, vol. 123, pp. 413 - 425, http://dx.doi.org/10.1016/j.jnt.2006.07.011

Becheanu M; Luca F; Shparlinski IE, 2007, 'On the sums of complementary divisors', INTERNATIONAL JOURNAL OF NUMBER THEORY, vol. 3, pp. 635 - 648, http://dx.doi.org/10.1142/S1793042107001152

Blackburn SR; Shparlinski IE, 2007, 'Erratum to "Character sums and nonlinear recurrence sequences". [Discrete Math. 306 (2006) 1126-1131] (DOI:10.1016/j.disc.2006.02.012)', Discrete Mathematics, vol. 307, pp. 1218 - 1219, http://dx.doi.org/10.1016/j.disc.2006.10.009

Blake IF; Shparlinski IE, 2007, 'Statistical distribution and collisions of VSH', JOURNAL OF MATHEMATICAL CRYPTOLOGY, vol. 1, pp. 329 - 349, http://dx.doi.org/10.1515/JMC.2007.016

Friedlander JB; Shparlinski IE, 2007, 'Least totient in a residue class', Bulletin of the London Mathematical Society, vol. 39, pp. 425 - 432, http://dx.doi.org/10.1112/blms/bdm027

Garaev MZ; Luca F; Shparlinski IE, 2007, 'Exponential sums with Catalan numbers and middle binomial coefficients', Indagationes Mathematicae, vol. 18, pp. 23 - 37, http://dx.doi.org/10.1016/S0019-3577(07)80004-8

Lange T; Shparlinski IE, 2007, 'Distribution of some sequences of points on elliptic curves', Journal of Mathematical Cryptology, vol. 1, pp. 1 - 11, http://dx.doi.org/10.1515/JMC.2007.001

Luca F; Shparlinski IE, 2007, 'Arithmetic functions with linear recurrence sequences', Journal of Number Theory, vol. 125, pp. 459 - 472, http://dx.doi.org/10.1016/j.jnt.2006.12.006

Luca F; Shparlinski IE, 2007, 'Discriminants of complex multiplication fields of elliptic curves over finite fields', Canadian Mathematical Bulletin, vol. 50, pp. 409 - 417, http://dx.doi.org/10.4153/CMB-2007-039-2

Luca F; Shparlinski IE, 2007, 'On finite fields for pairing based cryptography', ADVANCES IN MATHEMATICS OF COMMUNICATIONS, vol. 1, pp. 281 - 286, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000254707500001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Luca F; Shparlinski IE, 2007, 'On the square-free parts of ⌊en!⌋', Glasgow Mathematical Journal, vol. 49, pp. 391 - 403, http://dx.doi.org/10.1017/S0017089507003734

Luca F; Shparlinski IE, 2007, 'Pseudoprime Cullen and Woodall numbers', Colloquium Mathematicum, vol. 107, pp. 35 - 43, http://dx.doi.org/10.4064/cm107-1-5

Saxena N; Severini S; Shparlinski I, 2007, 'Parameters of integral circulant graphs and periodic quantum dynamics', International Journal of Quantum Information, vol. 5, pp. 417 - 430, http://dx.doi.org/10.1142/S0219749907002918

Shparlinski I, 2007, 'A computational introduction to number theory and algebra', MATHEMATICS OF COMPUTATION, vol. 76, pp. 1697 - 1698, http://dx.doi.org/10.1090/S0025-5718-07-01995-3

Shparlinski IE, 2007, 'Bounds of incomplete multiple Kloosterman sums', JOURNAL OF NUMBER THEORY, vol. 126, pp. 68 - 73, http://dx.doi.org/10.1016/j.jnt.2006.12.003

Shparlinski IE, 2007, 'Bounds of incomplete multiple Kloosterman sums', Journal of Number Theory, vol. 126, pp. 68 - 73, http://dx.doi.org/10.1016/j.jnt.2006.12.003

Shparlinski IE, 2007, 'Bounds on the Fourier coefficients of the weighted sum function', Information Processing Letters, vol. 103, pp. 83 - 87, http://dx.doi.org/10.1016/j.ipl.2007.02.011

Shparlinski IE, 2007, 'Character sums over shifted smooth numbers', Proceedings of the American Mathematical Society, vol. 135, pp. 2699 - 2705, http://dx.doi.org/10.1090/S0002-9939-07-08785-0

Shparlinski IE, 2007, 'Communication complexity of some number theoretic functions', Applied Mathematics Letters, vol. 20, pp. 872 - 875, http://dx.doi.org/10.1016/j.aml.2006.05.024

Shparlinski IE, 2007, 'Distribution of roots of polynomial congruences', International Journal of Mathematics and Mathematical Sciences, vol. 2007, http://dx.doi.org/10.1155/2007/37853

Shparlinski IE, 2007, 'On some dynamical systems in finite fields and residue rings', Discrete and Continuous Dynamical Systems, vol. 17, pp. 901 - 917, http://dx.doi.org/10.3934/dcds.2007.17.901

Shparlinski IE, 2007, 'On the distribution of angles of the salié sums', Bulletin of the Australian Mathematical Society, vol. 75, pp. 221 - 227, http://dx.doi.org/10.1017/s0004972700039150

Shparlinski IE, 2007, 'On the distribution of points on multidimensional modular hyperbolas', Proceedings of the Japan Academy Series A: Mathematical Sciences, vol. 83, pp. 5 - 9, http://dx.doi.org/10.3792/pjaa.83.5

Shparlinski IE; Steinfeld R, 2007, 'Chinese remaindering with multiplicative noise', Theory of Computing Systems, vol. 40, pp. 33 - 41, http://dx.doi.org/10.1007/s00224-005-1272-9

Shparlinski IE; Sutantyo D, 2007, 'On the set of the largest prime divisors', Publicationes Mathematicae, vol. 71, pp. 95 - 100

Shparlinski IE; Voloch JF, 2007, 'Visible Points on Curves over Finite Fields', Bulletin of the Polish Academy of Sciences Mathematics, vol. 55, pp. 193 - 199, http://dx.doi.org/10.4064/ba55-3-1

Shparlinski IE; Winterhof A, 2007, 'Quantum period reconstruction of approximate sequences', Information Processing Letters, vol. 103, pp. 211 - 215, http://dx.doi.org/10.1016/j.ipl.2007.02.019

Banks MK, 2006, 'Editor’s Note', Journal of Environmental Engineering, vol. 132, pp. 157 - 157, http://dx.doi.org/10.1061/(asce)0733-9372(2006)132:2(157)

Banks WD; Friedlander JB; Garaev MZ; Shparlinski IE, 2006, 'Character sums with exponential functions over smooth numbers', Indagationes Mathematicae, vol. 17, pp. 157 - 168, http://dx.doi.org/10.1061/(ASCE)0733-9372(2006)132:2(157)

Banks WD; Friedlander JB; Garaev MZ; Shparlinski IE, 2006, 'Double character sums over elliptic curves and finite fields', PURE AND APPLIED MATHEMATICS QUARTERLY, vol. 2, pp. 179 - 197, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000241377300008&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Banks WD; Friedlander JB; Konyagin SV; Shparlinski IE, 2006, 'Incomplete exponential sums and Diffie-Hellman triples', Mathematical Proceedings of the Cambridge Philosophical Society, vol. 140, pp. 193 - 206, http://dx.doi.org/10.1017/S0305004105008947

Banks WD; Friedlander JB; Luca F; Pappalardi F; Shparlinski IE, 2006, 'Coincidences in the values of the Euler and Carmichael functions', Acta Arithmetica, vol. 122, pp. 207 - 234, http://dx.doi.org/10.4064/aa122-3-1

Banks WD; Luca F; Shparlinski IE, 2006, 'Arithmetic properties of φ(n)/λ(n) and the structure of the multiplicative group modulo n', Commentarii Mathematici Helvetici, vol. 81, pp. 1 - 22, http://dx.doi.org/10.4171/CMH/40

Banks WD; Luca F; Shparlinski IE, 2006, 'Common divisors of the Euler function at related arguments', ACTA SCIENTIARUM MATHEMATICARUM, vol. 72, pp. 525 - 536, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000216758800005&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Banks WD; Shparlinski IE, 2006, 'Average Value of the Euler Function on Binary Palindromes', Bulletin of the Polish Academy of Sciences Mathematics, vol. 54, pp. 95 - 101, http://dx.doi.org/10.4064/ba54-2-1

Banks WD; Shparlinski IE, 2006, 'Character sums with Beatty sequences on Burgess-type intervals', Character sums with Beatty sequences on Burgess-type intervals, http://arxiv.org/abs/math/0608042v1

Banks WD; Shparlinski IE, 2006, 'Congruences and rational exponential sums with the euler function', Rocky Mountain Journal of Mathematics, vol. 36, pp. 1415 - 1426, http://dx.doi.org/10.1216/rmjm/1181069373

Banks WD; Shparlinski IE, 2006, 'Integers with a large smooth divisor', Integers with a large smooth divisor, http://arxiv.org/abs/math/0601460v1

Banks WD; Shparlinski IE, 2006, 'Multiplicative character sums with the sum of g-ary digits function', Ramanujan Journal, vol. 11, pp. 215 - 219, http://dx.doi.org/10.1007/s11139-006-6508-z

Banks WD; Shparlinski IE, 2006, 'Non-residues and primitive roots in beatty sequences', Bulletin of the Australian Mathematical Society, vol. 73, pp. 433 - 443, http://dx.doi.org/10.1017/s0004972700035449

Banks WD; Shparlinski IE, 2006, 'Short character sums with beatty sequences', Mathematical Research Letters, vol. 13, pp. 539 - 547, http://dx.doi.org/10.4310/MRL.2006.v13.n4.a4

Blackburn SR; Gomez-Perez D; Gutierrez J; Shparlinski IE, 2006, 'Reconstructing noisy polynomial evaluation in residue rings', JOURNAL OF ALGORITHMS-COGNITION INFORMATICS AND LOGIC, vol. 61, pp. 47 - 59, http://dx.doi.org/10.1016/j.jalgor.2004.07.002

Blackburn SR; Gomez-Perez D; Gutierrez J; Shparlinski IE, 2006, 'Reconstructing noisy polynomial evaluation in residue rings', Journal of Algorithms, vol. 61, pp. 47 - 59, http://dx.doi.org/10.1016/j.jalgor.2004.07.002

Blackburn SR; Shparlinski IE, 2006, 'Character sums and nonlinear recurrence sequences', Discrete Mathematics, vol. 306, pp. 1126 - 1131, http://dx.doi.org/10.1016/j.disc.2006.02.012

Blake IF; Garefalakis T; Shparlinski IE, 2006, 'On the bit security of the Diffie-Hellman key', Applicable Algebra in Engineering, Communications and Computing, vol. 16, pp. 397 - 404, http://dx.doi.org/10.1007/s00200-005-0184-x

Contini S; Croot E; Shparlinski IE, 2006, 'Complexity of inverting the Euler function', Mathematics of Computation, vol. 75, pp. 983 - 996, http://dx.doi.org/10.1090/S0025-5718-06-01826-6

Coppersmith D; Howgrave-Graham N; Nguyễn PQ; Shparlinski IE, 2006, 'Testing set proportionality and the Ádám isomorphism of circulant graphs', Journal of Discrete Algorithms, vol. 4, pp. 324 - 335, http://dx.doi.org/10.1016/j.jda.2005.06.003

El-Mahassni ED; Shparlinski IE; Winterhof A, 2006, 'Distribution of nonlinear congruential pseudorandom numbers modulo almost squarefree integers', Monatshefte fur Mathematik, vol. 148, pp. 297 - 307, http://dx.doi.org/10.1007/s00605-005-0355-7

Garaev MZ; Luca F; Shparlinski IE, 2006, 'Catalan and Apéry numbers in residue classes', Journal of Combinatorial Theory. Series A, vol. 113, pp. 851 - 865, http://dx.doi.org/10.1016/j.jcta.2005.08.003

Garaev MZ; Luca F; Shparlinski IE, 2006, 'Distribution of harmonic sums and Bernoulli polynomials modulo a prime', Mathematische Zeitschrift, vol. 253, pp. 855 - 865, http://dx.doi.org/10.1007/s00209-006-0939-5

Garaev MZ; Luca F; Shparlinski IE; Winterhof A, 2006, 'On the lower bound of the linear complexity over Fp of Sidelnikov sequences', IEEE Transactions on Information Theory, vol. 52, pp. 3299 - 3304, http://dx.doi.org/10.1109/TIT.2006.876352

Gomez-Perez D; Gutierrez J; Shparlinski IE, 2006, 'Exponential sums with Dickson polynomials', Finite Fields and their Applications, vol. 12, pp. 16 - 25, http://dx.doi.org/10.1016/j.ffa.2004.08.001

Luca F; McKee J; Shparlinsk IE, 2006, 'Small exponent point groups on elliptic curves', Journal de Theorie des Nombres de Bordeaux, vol. 18, pp. 471 - 476, http://dx.doi.org/10.5802/jtnb.554

Luca F; Shparlinski IE, 2006, 'Arithmetic properties of the Ramanujan function', Proceedings of the Indian Academy of Sciences: Mathematical Sciences, vol. 116, pp. 1 - 8, http://dx.doi.org/10.1007/BF02829735

Luca F; Shparlinski IE, 2006, 'Elliptic curves with low embedding degree', Journal of Cryptology, vol. 19, pp. 553 - 562, http://dx.doi.org/10.1007/s00145-006-0544-0

Luca F; Shparlinski IE, 2006, 'ON THE NUMBER OF POLYNOMIAL MAPS INTO Z(n)', TSUKUBA JOURNAL OF MATHEMATICS, vol. 30, pp. 431 - 441, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000219852100011&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Luca F; Shparlinski IE, 2006, 'On the number of polynomial maps into $\mathbb{Z}_{n}$', Tsukuba Journal of Mathematics, vol. 30, http://dx.doi.org/10.21099/tkbjm/1496165073

Luca F; Shparlinski IE, 2006, 'Pseudoprime values of the Fibonacci sequence, polynomials and the Euler function', Indagationes Mathematicae, vol. 17, pp. 611 - 625, http://dx.doi.org/10.1016/S0019-3577(06)81037-2

Luca F; Shparlinski IE, 2006, 'Some divisibilities amongst the terms of linear recurrences', Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg, vol. 76, pp. 143 - 156, http://dx.doi.org/10.1007/BF02960862

Luca F; Shparlinski IE, 2006, 'Uniformity of distribution modulo 1 of the geometric mean prime divisor', Boletin de la Sociedad Matematica Mexicana, vol. 12, pp. 155 - 163

Shparlinski I, 2006, 'On the energy of some circulant graphs', Linear Algebra and Its Applications, vol. 414, pp. 378 - 382, http://dx.doi.org/10.1016/j.laa.2005.10.020

Shparlinski I, 2006, 'On the set of distances between two sets over finite fields', International Journal of Mathematics and Mathematical Sciences, vol. 2006, http://dx.doi.org/10.1155/IJMMS/2006/59482

Shparlinski IE, 2006, 'On RSA moduli with prescribed bit patterns', Designs, Codes, and Cryptography, vol. 39, pp. 113 - 122, http://dx.doi.org/10.1007/s10623-005-3137-2

Shparlinski IE, 2006, 'On some generalisations of the Erdos distance problem over finite fields', Bulletin of the Australian Mathematical Society, vol. 73, pp. 285 - 292, http://dx.doi.org/10.1017/S0004972700038867

Shparlinski IE, 2006, 'On the sum of iterations of the Euler function', Journal of Integer Sequences, vol. 9, pp. 1 - 5

Shparlinski IE, 2006, 'Primitive Points on a Modular Hyperbola', Bulletin of the Polish Academy of Sciences Mathematics, vol. 54, pp. 193 - 200, http://dx.doi.org/10.4064/ba54-3-1

Shparlinski IE, 2006, 'Truncations of L-functions in residue classes', Glasgow Mathematical Journal, vol. 48, pp. 347 - 350, http://dx.doi.org/10.1017/S0017089506003120

Shparlinski IE; Winterhof A, 2006, 'Constructions of approximately mutually unbiased bases', Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 3887 LNCS, pp. 793 - 799, http://dx.doi.org/10.1007/11682462_72

Shparlinski IE; Winterhof A, 2006, 'On the discrepancy and linear complexity of some counter-dependent recurrence sequences', Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4086 LNCS, pp. 295 - 303, http://dx.doi.org/10.1007/11863854_25

Shparlinski IE; Winterhof A, 2006, 'On the nonlinearity of linear recurrence sequences', Applied Mathematics Letters, vol. 19, pp. 340 - 344, http://dx.doi.org/10.1016/j.aml.2005.04.015

Von Zur Gathen J; Shparlinski IE, 2006, 'GCD of random linear combinations', Algorithmica (New York), vol. 46, pp. 137 - 148, http://dx.doi.org/10.1007/s00453-006-0072-1

Banks WD; Ford K; Luca F; Pappalardi F; Shparlinski IE, 2005, 'Values of the Euler function in various sequences', Monatshefte fur Mathematik, vol. 146, pp. 1 - 19, http://dx.doi.org/10.1007/s00605-005-0302-7

Banks WD; Garaev MZ; Luca F; Shparlinski IE, 2005, 'Uniform Distribution of the Fractional Part of the Average Prime Divisor', Forum Mathematicum, vol. 17, pp. 885 - 901, http://dx.doi.org/10.1515/form.2005.17.6.885

Banks WD; Harman G; Shparlinski IE, 2005, 'Distributional properties of the largest prime factor', Michigan Mathematical Journal, vol. 53, pp. 665 - 681, http://dx.doi.org/10.1307/mmj/1133894172

Banks WD; Heath-Brown R; Shparlinski IE, 2005, 'On the average value of divisor sums in arithmetic progressions', International Mathematics Research Notices, pp. 1 - 25, http://dx.doi.org/10.1155/imrn.2005.1

Banks WD; Luca F; Saidak F; Shparlinski IE, 2005, 'Values of arithmetical functions equal to a sum of two squares', Quarterly Journal of Mathematics, vol. 56, pp. 123 - 139, http://dx.doi.org/10.1093/qmath/hah039

Banks WD; Luca F; Shparlinski IE, 2005, 'Irrationality of power series for various number theoretic functions', Manuscripta Mathematica, vol. 117, pp. 183 - 197, http://dx.doi.org/10.1007/s00229-005-0564-3

Banks WD; Luca F; Shparlinski IE, 2005, 'Some divisibility properties of the Euler function', Glasgow Mathematical Journal, vol. 47, pp. 517 - 528, http://dx.doi.org/10.1017/S0017089505002752

Banks WD; Shparlinski IE, 2005, 'Prime divisors of palindromes', Periodica Mathematica Hungarica, vol. 51, pp. 1 - 10, http://dx.doi.org/10.1007/s10998-005-0016-6

Blackburn SR; Gomez-Perez D; Gutierrez J; Shparlinski IE, 2005, 'Predicting nonlinear pseudorandom number generators', Mathematics of Computation, vol. 74, pp. 1471 - 1494, http://dx.doi.org/10.1090/S0025-5718-04-01698-9

Cohen SD; Dewar M; Friedlander JB; Panario D; Shparlinski IE, 2005, 'Polynomial gauss sums', Proceedings of the American Mathematical Society, vol. 133, pp. 2225 - 2231, http://dx.doi.org/10.1090/S0002-9939-05-08004-4

Contini S; Shparlinski IE, 2005, 'On Stern's attack against secret truncated linear congruential generators', Lecture Notes in Computer Science, vol. 3574, pp. 52 - 60, http://dx.doi.org/10.1007/11506157_5

De Koninck JM; Luca F; Shparlinski IE, 2005, 'Powerful numbers in short intervals', Bulletin of the Australian Mathematical Society, vol. 71, pp. 11 - 16, http://dx.doi.org/10.1017/s0004972700037953

Everest G; Shparlinski IE, 2005, 'Prime divisors of sequences associated to elliptic curves', Glasgow Mathematical Journal, vol. 47, pp. 115 - 122, http://dx.doi.org/10.1017/S0017089504002113

Ford K; Khan MR; Shparlinski IE; Yankov CL, 2005, 'On the maximal difference between an element and its inverse in residue rings', Proceedings of the American Mathematical Society, vol. 133, pp. 3463 - 3468, http://dx.doi.org/10.1090/S0002-9939-05-07962-1

Friedlander JB; Pomerance C; Shparlinski IE, 2005, 'Finding the group structure of elliptic curves over finite fields', Bulletin of the Australian Mathematical Society, vol. 72, pp. 251 - 263, http://dx.doi.org/10.1017/s0004972700035048

Garaev MZ; Luca F; Shparlinski IE, 2005, 'Exponential sums and congruences with factorials', Journal fur die Reine und Angewandte Mathematik, pp. 29 - 44, http://dx.doi.org/10.1515/crll.2005.2005.584.29

Garaev MZ; Luca F; Shparlinski IE, 2005, 'Waring problem with factorials', Bulletin of the Australian Mathematical Society, vol. 71, pp. 259 - 264, http://dx.doi.org/10.1017/s0004972700038223

Garaev MZ; Shparlinski IE, 2005, 'The large sieve inequality with exponential functions and the distribution of mersenne numbers modulo primes', International Mathematics Research Notices, pp. 2391 - 2403, http://dx.doi.org/10.1155/imrn.2005.2391

Granville A; Shparlinski IE; Zaharescu A, 2005, 'On the distribution of rational functions along a curve over F-P and residue races', JOURNAL OF NUMBER THEORY, vol. 112, pp. 216 - 237, http://dx.doi.org/10.1016/j.jnt.2005.02.002

Granville A; Shparlinski IE; Zaharescu A, 2005, 'On the distribution of rational functions along a curve over Fp and residue races', Journal of Number Theory, vol. 112, pp. 216 - 237, http://dx.doi.org/10.1016/j.jnt.2005.02.002

Hallgren S; Russell A; Shparlinski IE, 2005, 'Quantum noisy rational function reconstruction', Lecture Notes in Computer Science, vol. 3595, pp. 420 - 429, http://dx.doi.org/10.1007/11533719_43

Hess F; Shparlinski IE, 2005, 'On the linear complexity and multidimensional distribution of congruential generators over elliptic curves', Designs, Codes, and Cryptography, vol. 35, pp. 111 - 117, http://dx.doi.org/10.1007/s10623-003-6153-0

Klappenecker A; Rötteler M; Shparlinski IE; Winterhof A, 2005, 'On approximately symmetric informationally complete positive operator-valued measures and related systems of quantum states', Journal of Mathematical Physics, vol. 46, http://dx.doi.org/10.1063/1.1998831

Lange T; Shparlinski I, 2005, 'Collisions in fast generation of ideal classes and points on hyperelliptic and elliptic curves', Applicable Algebra in Engineering, Communications and Computing, vol. 15, pp. 329 - 337, http://dx.doi.org/10.1007/s00200-004-0161-9

Lange T; Shparlinski IE, 2005, 'Certain exponential sums and random walks on elliptic curves', Canadian Journal of Mathematics, vol. 57, pp. 338 - 350, http://dx.doi.org/10.4153/CJM-2005-015-8

Levieil E; Luca F; Shparlinski IE, 2005, 'Bounding the number of solutions of some congruences', Boletin de la Sociedad Matematica Mexicana, vol. 11, pp. 175 - 180

Levieil E; Luca F; Shparlinski IE, 2005, 'Prime divisors of some shifted products', International Journal of Mathematics and Mathematical Sciences, vol. 2005, pp. 3057 - 3073, http://dx.doi.org/10.1155/IJMMS.2005.3057

Luca F; Shparlinski IE, 2005, 'On the exponent of the group of points on elliptic curves in extension fields', International Mathematics Research Notices, pp. 1391 - 1409, http://dx.doi.org/10.1155/imrn.2005.1391

Luca F; Shparlinski IE, 2005, 'On the largest prime factor of n! + 2ⁿ − 1', Journal de Theorie des Nombres de Bordeaux, vol. 17, pp. 859 - 870, http://dx.doi.org/10.5802/jtnb.524

Luca F; Shparlinski IE, 2005, 'Prime divisors of shifted factorials', Bulletin of the London Mathematical Society, vol. 37, pp. 809 - 817, http://dx.doi.org/10.1112/S0024609305004923

Shparlinski I, 2005, 'Book Review: Report on global methods for combinatorial isoperimetric problems', Mathematics of Computation, vol. 74, pp. 1033 - 1052, http://dx.doi.org/10.1090/s0025-5718-04-01757-0

Shparlinski I; Winterhof A, 2005, 'A hidden number problem in small subgroups', Mathematics of Computation, vol. 74, pp. 2073 - 2080, http://dx.doi.org/10.1090/S0025-5718-05-01797-7

Shparlinski I; Winterhof A, 2005, 'Noisy interpolation of sparse polynomials in finite fields', Applicable Algebra in Engineering, Communications and Computing, vol. 16, pp. 307 - 317, http://dx.doi.org/10.1007/s00200-005-0180-1

Shparlinski IE, 2005, 'On the nonlinearity of the sequence of signs of Kloosterman sums', Bulletin of the Australian Mathematical Society, vol. 71, pp. 405 - 409, http://dx.doi.org/10.1017/s0004972700038405

Shparlinski IE, 2005, 'On the singularity of generalised Vandermonde matrices over finite fields', Finite Fields and their Applications, vol. 11, pp. 193 - 199, http://dx.doi.org/10.1016/j.ffa.2004.11.001

Shparlinski IE, 2005, 'On the value set of the Ramanujan function', Archiv der Mathematik, vol. 85, pp. 508 - 513, http://dx.doi.org/10.1007/s00013-005-1322-1

Shparlinski IE; Winterhof A, 2005, 'On the linear complexity of bounded integer sequences over different moduli', Information Processing Letters, vol. 96, pp. 175 - 177, http://dx.doi.org/10.1016/j.ipl.2005.08.004

Banks WD; Conflitti A; Friedlander JB; Shparlinski IE, 2004, 'Exponential sums over Mersenne numbers', Compositio Mathematica, vol. 140, pp. 15 - 30, http://dx.doi.org/10.1112/S0010437X03000022

Banks WD; Conflitti A; Shparlinski IE, 2004, 'Number theoretic designs for directed regular graphs of small diameter', SIAM Journal on Discrete Mathematics, vol. 17, pp. 377 - 383, http://dx.doi.org/10.1137/S0895480101396676

Banks WD; Harcharras A; Shparlinski IE, 2004, 'Smooth values of shifted primes in arithmetic progressions', Michigan Mathematical Journal, vol. 52, pp. 603 - 618, http://dx.doi.org/10.1307/mmj/1100623415

Banks WD; Shparlinski IE, 2004, 'Arithmetic properties of numbers with restricted digits', Acta Arithmetica, vol. 112, pp. 313 - 332, http://dx.doi.org/10.4064/aa112-4-1

Chou WS; Shparlinski IE, 2004, 'On the cycle structure of repeated exponentiation modulo a prime', Journal of Number Theory, vol. 107, pp. 345 - 356, http://dx.doi.org/10.1016/j.jnt.2004.04.005

Conflitti A; Shparlinski IE, 2004, 'On the multidimensional distribution of the subset sum generator of pseudorandom numbers', Mathematics of Computation, vol. 73, pp. 1005 - 1011, http://dx.doi.org/10.1090/S0025-5718-03-01563-1

Dewar M; Panario D; Shparlinski IE, 2004, 'Distribution of exponential functions with k-full exponent modulo a prime', Indagationes Mathematicae, vol. 15, pp. 497 - 503, http://dx.doi.org/10.1016/S0019-3577(04)80014-4

Frandsen GS; Shparlinski IE, 2004, 'On Reducing a System of Equations to a Single Equation', BRICS Report Series, vol. 11, http://dx.doi.org/10.7146/brics.v11i6.21831

Frandsen GS; Shparlinski IE, 2004, 'On reducing a system of equations to a single equation', Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC, pp. 163 - 166, http://dx.doi.org/10.1145/1005285.1005310

Galbraith SD; Hopkins HJ; Shparlinski IE, 2004, 'Secure bilinear Diffie-Hellman bits', Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 3108, pp. 370 - 378, http://dx.doi.org/10.1007/978-3-540-27800-9_32

Garaev MZ; Luca F; Shparlinski IE, 2004, 'Character sums and congruences with n!', Transactions of the American Mathematical Society, vol. 356, pp. 5089 - 5102, http://dx.doi.org/10.1090/S0002-9947-04-03612-8

Goresky M; Klapper A; Murty R; Shparlinski I, 2004, 'On decimations of ℓ-sequences', SIAM Journal on Discrete Mathematics, vol. 18, pp. 130 - 140, http://dx.doi.org/10.1137/S0895480102403428

Luca F; Mireles DJ; Shparlinski IE, 2004, 'Florianptic curves', Illinois Journal of Mathematics, vol. 48, pp. 1041 - 1052, http://dx.doi.org/10.1215/ijm/1258131069

Luca F; Mireles DJ; Shparlinski IE, 2004, 'Mov attack in various subgroups on elliptic curves', ILLINOIS JOURNAL OF MATHEMATICS, vol. 48, pp. 1041 - 1052, http://dx.doi.org/10.1215/ijm/1258131069

Mans B; Shparlinski I, 2004, 'Bisecting and gossiping in circulant graphs', Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 2976, pp. 589 - 598, http://dx.doi.org/10.1007/978-3-540-24698-5_61

Russell A; Shparlinski IE, 2004, 'Classical and quantum function reconstruction via character evaluation', Journal of Complexity, vol. 20, pp. 404 - 422, http://dx.doi.org/10.1016/j.jco.2003.08.019

Shparlinski IE, 2004, 'Bounds of Gauss sums in finite fields', Proceedings of the American Mathematical Society, vol. 132, pp. 2817 - 2824, http://dx.doi.org/10.1090/S0002-9939-04-07133-3

Shparlinski IE, 2004, 'Distribution of exponential functions with squarefull exponent in residue rings', Indagationes Mathematicae, vol. 15, pp. 283 - 289, http://dx.doi.org/10.1016/S0019-3577(04)90020-1

Shparlinski IE, 2004, 'Exponential function analogue of kloosterman sums', Rocky Mountain Journal of Mathematics, vol. 34, pp. 1497 - 1502, http://dx.doi.org/10.1216/rmjm/1181069811

Shparlinski IE, 2004, 'On the uniformity of distribution of the decryption exponent in fixed encryption exponent RSA', Information Processing Letters, vol. 92, pp. 143 - 147, http://dx.doi.org/10.1016/j.ipl.2004.07.004

Shparlinski IE, 2004, 'Security of polynomial transformations of the Diffie-Hellman key', Finite Fields and their Applications, vol. 10, pp. 123 - 131, http://dx.doi.org/10.1016/S1071-5797(03)00048-0

Shparlinski IE; Steinfield R, 2004, 'Noisy Chinese remaindering in the Lee norm', Journal of Complexity, vol. 20, pp. 423 - 437, http://dx.doi.org/10.1016/j.jco.2003.08.020

Shparlinski IE; Winterhof A, 2004, 'A nonuniform algorithm for the hidden number problem in subgroups', Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 2947, pp. 416 - 424, http://dx.doi.org/10.1007/978-3-540-24632-9_30

Vasco MIG; Näslund M; Shparlinski IE, 2004, 'New results on the hardness of diffie-hellman bits', Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 2947, pp. 159 - 172

Von Gathen JZ; Shparlinski IE, 2004, 'GCD of random linear forms', Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 3341, pp. 464 - 469

Von Gathen JZ; Shparlinski IE, 2004, 'Predicting Subset Sum Pseudorandom Generators', Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 3357, pp. 241 - 251

Von Gathen JZ; Shparlinski IE, 2004, 'Predicting Subset Sum Pseudorandom Generators', Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 3357, pp. 241 - 251

Von Zur Gathen J; Shparlinski IE, 2004, 'Polynomial Interpolation from Multiples', Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, vol. 15, pp. 1125 - 1130

von zur Gathen J; Knopfmacher A; Luca F; Lucht LG; Shparlinski IE, 2004, 'Average order in cyclic groups', Journal de Theorie des Nombres de Bordeaux, vol. 16, pp. 107 - 123, http://dx.doi.org/10.5802/jtnb.436

von zur Gathen J; Shparlinski I; Stichtenoth H, 2004, 'Finite Fields: Theory and Applications', Oberwolfach Reports, pp. 2913 - 2970, http://dx.doi.org/10.4171/owr/2004/54

Allender E; Bernasconi A; Damm C; Von Zur Gathen J; Saks M; Shparlinski I, 2003, 'Complexity of some arithmetic problems for binary polynomials', Computational Complexity, vol. 12, pp. 23 - 47, http://dx.doi.org/10.1007/s00037-003-0176-9

Banks WD; Harcharras A; Shparlinski IE, 2003, 'Short Kloosterman sums for polynomials over finite fields', Canadian Journal of Mathematics, vol. 55, pp. 225 - 246, http://dx.doi.org/10.4153/CJM-2003-010-0

Blackburn SR; Gomez-Perez D; Gutierrez J; Shparlinski IE, 2003, 'Predicting the Inversive Generator', Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 2898, pp. 264 - 275, http://dx.doi.org/10.1007/978-3-540-40974-8_21

Guruswami V; Shparlinski I, 2003, 'Unconditional proof of tightness of Johnson bound', Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 754 - 755

Gutierrez J; Shparlinski IE; Winterhof A, 2003, 'On the linear and nonlinear complexity profile of nonlinear pseudorandom number generators', IEEE Transactions on Information Theory, vol. 49, pp. 60 - 64, http://dx.doi.org/10.1109/TIT.2002.806144

Howgrave-Graham NA; Nguyen PQ; Shparlinski IE, 2003, 'Hidden number problem with hidden multipliers, timed-release crypto, and noisy exponentiation', Mathematics of Computation, vol. 72, pp. 1473 - 1485, http://dx.doi.org/10.1090/S0025-5718-03-01495-9

Khan MR; Shparlinski IE, 2003, 'On the maximal difference between an element and its inverse modulo n', Periodica Mathematica Hungarica, vol. 47, pp. 111 - 117, http://dx.doi.org/10.1023/b:mahu.0000010815.14847.96

Konyagin S; Lange T; Shparlinski I, 2003, 'Linear complexity of the discrete logarithm', Designs, Codes, and Cryptography, vol. 28, pp. 135 - 146, http://dx.doi.org/10.1023/A:1022584306676

Luca F; Shparlinski IE, 2003, 'Average multiplicative orders of elements modulo n', Acta Arithmetica, vol. 109, pp. 387 - 411, http://dx.doi.org/10.4064/aa109-4-7

Nguyen PQ; Shparlinski IE, 2003, 'The Insecurity of the Elliptic Curve Digital Signature Algorithm with Partially Known Nonces', Designs, Codes, and Cryptography, vol. 30, pp. 201 - 217, http://dx.doi.org/10.1023/A:1025436905711

Nguyen PQ; Shparlinski IE, 2003, 'The insecurity of the digital signature algorithm with partially known nonces', Journal of Cryptology, vol. 15, pp. 151 - 176, http://dx.doi.org/10.1007/s00145-002-0021-3

Niederreiter H; Shparlinski IE, 2003, 'Dynamical systems generated by rational functions', Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 2643, pp. 6 - 17, http://dx.doi.org/10.1007/3-540-44828-4_2

Niederreiter H; Shparlinski IE, 2003, 'On the distribution of power residues and primitive elements in some nonlinear recurring sequences', Bulletin of the London Mathematical Society, vol. 35, pp. 522 - 528, http://dx.doi.org/10.1112/S002460930300198X

Niederreiter H; Shparlinski IE, 2003, 'Periodic sequences with maximal linear complexity and almost maximal k-rrror linear complexity', Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 2898, pp. 183 - 189, http://dx.doi.org/10.1007/978-3-540-40974-8_15

Näslund M; Shparlinski IE; Whyte W, 2003, 'On the bit security of NTRUEncrypt', Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 2567, pp. 62 - 70, http://dx.doi.org/10.1007/3-540-36288-6_5

Pappalardi F; Saidak F; Shparlinski IE, 2003, 'Square-free values of the Carmichael function', Journal of Number Theory, vol. 103, pp. 122 - 131, http://dx.doi.org/10.1016/S0022-314X(03)00110-0

Shparlinski IE, 2003, 'Prime divisors of sparse integers', Periodica Mathematica Hungarica, vol. 46, pp. 215 - 222, http://dx.doi.org/10.1023/A:1025996312037

Von Zur Gathen J; Shparlinski I; Sinclair A, 2003, 'Finding points on curves over finite fields', SIAM Journal on Computing, vol. 32, pp. 1436 - 1448, http://dx.doi.org/10.1137/S0097539799351018

Banks WD; Conflitti A; Shparlinski IE, 2002, 'Character sums over integers with restricted g-ary digits', Illinois Journal of Mathematics, vol. 46, pp. 819 - 836, http://dx.doi.org/10.1215/ijm/1258130986

Banks WD; Shparlinski IE, 2002, 'Average normalisations of elliptic curves', Bulletin of the Australian Mathematical Society, vol. 66, pp. 353 - 358, http://dx.doi.org/10.1017/s0004972700040211

Banks WD; Shparlinski IE, 2002, 'On the number of sparse RSA exponents', JOURNAL OF NUMBER THEORY, vol. 95, pp. 340 - 350, http://dx.doi.org/10.1006/jnth.2001.2775

Banks WD; Shparlinski IE, 2002, 'On the number of sparse RSA exponents', Journal of Number Theory, vol. 95, pp. 340 - 350, http://dx.doi.org/10.1016/S0022-314X(01)92775-1

Codenotti B; Shparlinski IE; Winterhof A, 2002, 'On the hardness of approximating the permanent of structured matrices', Computational Complexity, vol. 11, pp. 158 - 170, http://dx.doi.org/10.1007/s00037-002-0174-3

El Mahassni E; Shparlinski I, 2002, 'On the Uniformity of Distribution of the Elliptic Curve ElGamal Signature', Finite Fields and Their Applications, vol. 8, pp. 589 - 596, http://dx.doi.org/10.1006/ffta.2002.0366

El Mahassni E; Shparlinski I, 2002, 'On the uniformity of distribution of the elliptic curve ElGamal signature', Finite Fields and their Applications, vol. 8, pp. 589 - 596, http://dx.doi.org/10.1006/ffta.2002.0366

Friedlander JB; Konyagin S; Shparllnski IE, 2002, 'Some doubly exponential sums over ℤm', Acta Arithmetica, vol. 105, pp. 349 - 370, http://dx.doi.org/10.4064/aa105-4-4

Friedlander JB; Pomerance C; Shparlinski IE, 2002, 'Erratum: Period of the power generator and small values of Carmichael's function (Mathematics of Computation)', Mathematics of Computation, vol. 71, pp. 1803 - 1806, http://dx.doi.org/10.1090/S0025-5718-02-01519-3

Mans B; Pappalardi F; Shparlinski I, 2002, 'On the spectral Ádám property for circulant graphs', Discrete Mathematics, vol. 254, pp. 309 - 329, http://dx.doi.org/10.1016/S0012-365X(01)00374-0

Niederreiter H; Shparlinski IE, 2002, 'On the Average Distribution of Inversive Pseudorandom Numbers', Finite Fields and Their Applications, vol. 8, pp. 491 - 503, http://dx.doi.org/10.1006/ffta.2002.0358

Niederreiter H; Shparlinski IE, 2002, 'On the average distribution of inversive pseudorandom numbers', Finite Fields and their Applications, vol. 8, pp. 491 - 503, http://dx.doi.org/10.1006/ffta.2002.0358

Shparlinski IE, 2002, 'On a question of Erdos and Graham', Archiv der Mathematik, vol. 78, pp. 445 - 448, http://dx.doi.org/10.1007/s00013-002-8269-2

Shparlinski IE, 2002, 'On the distribution of the Diffie-Hellman pairs', Finite Fields and their Applications, vol. 8, pp. 131 - 141, http://dx.doi.org/10.1006/ffta.2000.0321

Shparlinski IE, 2002, 'On the uniformity of distribution of the EIGamal signature', Applicable Algebra in Engineering, Communications and Computing, vol. 13, pp. 9 - 16, http://dx.doi.org/10.1007/s002000100087

Shparlinski IE, 2002, 'Security of most significant bits of g^x(2)', Information Processing Letters, vol. 83, pp. 109 - 113, http://dx.doi.org/10.1016/S0020-0190(01)00315-5

Vasco MIG; Shparlinski IE, 2002, 'Security of the most significant bits of the Shamir message passing scheme', Mathematics of Computation, vol. 71, pp. 333 - 342, http://dx.doi.org/10.1090/S0025-5718-01-01358-8

Banks WD; Shparlinski IE, 2001, 'Distribution of inverses in polynomial rings', Indagationes Mathematicae, vol. 12, pp. 303 - 315, http://dx.doi.org/10.1016/S0019-3577(01)80012-4

Bernasconi A; Damm C; Shparlinski I, 2001, 'Circuit and decision tree complexity of some number theoretic problems', Information and Computation, vol. 168, pp. 113 - 124, http://dx.doi.org/10.1006/inco.2000.3017

Boneh D; Shparlinski IE, 2001, 'On the unpredictability of bits of the elliptic curve Diffie-Hellman scheme', Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 2139 LNCS, pp. 201 - 212, http://dx.doi.org/10.1007/3-540-44647-8_12

Cohen SD; Niederreiter H; Shparlinski IE; Zieve M, 2001, 'Incomplete character sums and a special class of permutations', Journal de Theorie des Nombres de Bordeaux, vol. 13, pp. 53 - 63, http://dx.doi.org/10.5802/jtnb.303

El Mahassni E; Shparlinski I, 2001, 'On Some Uniformity of Distribution Properties of ESIGN', Electronic Notes in Discrete Mathematics, vol. 6, pp. 132 - 139, http://dx.doi.org/10.1016/S1571-0653(04)00164-7

El Mahassni E; Shparlinski I, 2001, 'Polynomial representations of the Diffie-Hellman mapping', Bulletin of the Australian Mathematical Society, vol. 63, pp. 467 - 473, http://dx.doi.org/10.1017/s0004972700019547

Friedlander JB; Pomerance C; Shparlinski IE, 2001, 'Period of the power generator and small values of Carmichael's function', Mathematics of Computation, vol. 70, pp. 1591 - 1605, http://dx.doi.org/10.1090/S0025-5718-00-01282-5

Friedlander JB; Shparlinsk IE, 2001, 'On the distribution of Diffie-Hellman triples with sparse exponents', SIAM Journal on Discrete Mathematics, vol. 14, pp. 162 - 169, http://dx.doi.org/10.1137/S0895480199361740

Friedlander JB; Shparlinski IE, 2001, 'Double exponential sums over thin sets', Proceedings of the American Mathematical Society, vol. 129, pp. 1617 - 1621, http://dx.doi.org/10.1090/s0002-9939-00-05921-9

Friedlander JB; Shparlinski IE, 2001, 'On the distribution of the power generator', Mathematics of Computation, vol. 70, pp. 1575 - 1589, http://dx.doi.org/10.1090/S0025-5718-00-01283-7

Lieman D; Shparlinski I, 2001, 'On a new exponential sum', Canadian Mathematical Bulletin, vol. 44, pp. 87 - 92, http://dx.doi.org/10.4153/CMB-2001-010-1

Niederreiter H; Shparlinski IE, 2001, 'On the distribution of inversive congruential pseudorandom numbers in parts of the period', Mathematics of Computation, vol. 70, pp. 1569 - 1574, http://dx.doi.org/10.1090/S0025-5718-00-01273-4

Shparlinski I, 2001, 'On Some Properties of the Shrinking Generator', Designs, Codes, and Cryptography, vol. 23, pp. 147 - 156, http://dx.doi.org/10.1023/A:1011256430812

Shparlinski I, 2001, 'On the Linear Complexity of the Power Generator', Designs, Codes, and Cryptography, vol. 23, pp. 5 - 10, http://dx.doi.org/10.1023/A:1011264815860

Shparlinski I, 2001, 'On the Multiplicative Orders of γ and γ+γ^-1 over finite fields', Finite Fields and their Applications, vol. 7, pp. 327 - 331, http://dx.doi.org/10.1006/ffta.2000.0292

Shparlinski IE, 2001, 'On the Uniformity of Distribution of the Naor-Reingold Pseudo-Random Function', Finite Fields and their Applications, vol. 7, pp. 318 - 326, http://dx.doi.org/10.1006/ffta.2000.0291

Shparlinski IE, 2001, 'On the uniformity of distribution of the RSA pairs', Mathematics of Computation, vol. 70, pp. 801 - 808, http://dx.doi.org/10.1090/S0025-5718-00-01274-6

Shparlinski IE, 2001, 'Sparse polynomial approximation in finite fields', Conference Proceedings of the Annual ACM Symposium on Theory of Computing, pp. 209 - 215, http://dx.doi.org/10.1145/380752.380803

Shparlinski IE; Silverman JH, 2001, 'On the Linear Complexity of the Naor-Reingold Pseudo-random Function from Elliptic Curves', Designs, Codes, and Cryptography, vol. 24, pp. 279 - 289, http://dx.doi.org/10.1023/A:1011223204345

Bernasconi A; Damm C; Shparlinski I, 2000, 'The average sensitivity of square-freeness', Computational Complexity, vol. 9, pp. 39 - 51, http://dx.doi.org/10.1007/PL00001600

Canetti R; Friedlander J; Konyagin S; Larsen M; Lieman D; Shparlinski I, 2000, 'On the statistical properties of Diffie-Hellman distributions', Israel Journal of Mathematics, vol. 120, pp. 23 - 46, http://dx.doi.org/10.1007/s11856-000-1270-1

Coppersmith D; Shparlinski I, 2000, 'On polynomial approximation of the discrete logarithm and the Diffie-Hellman mapping', JOURNAL OF CRYPTOLOGY, vol. 13, pp. 339 - 360, http://dx.doi.org/10.1007/s001450010002

El Mahassni E; Shparlinski I, 2000, 'On some uniformity of distribution properties of ESIGN', Electronic Notes in Discrete Mathematics, vol. 6, pp. 1 - 8

Friedlander JB; Hansen J; Shparlinski IE, 2000, 'Character sums with exponential functions', Mathematika, vol. 47, pp. 75 - 85, http://dx.doi.org/10.1112/S0025579300015734

Griffin F; Shparlinski IE, 2000, 'On the linear complexity profile of the power generator', IEEE Transactions on Information Theory, vol. 46, pp. 2159 - 2162, http://dx.doi.org/10.1109/18.868485

Gutierrez J; Niederreiter H; Shparlinski IE, 2000, 'On the multidimensional distribution of inversive congruential pseudorandom numbers in parts of the period', Monatshefte fur Mathematik, vol. 129, pp. 31 - 36, http://dx.doi.org/10.1007/s006050050004

Karpinski M; Van Der Poorten A; Shparlinski I, 2000, 'Zero testing of p-adic and modular polynomials', Theoretical Computer Science, vol. 233, pp. 309 - 317, http://dx.doi.org/10.1016/S0304-3975(99)00133-4

Niederreiter H; Shparlinski IE, 2000, 'Exponential sums and the distribution of inversive congruential pseudorandom numbers with prime-power modulus', Acta Arithmetica, vol. 92, pp. 89 - 98, http://dx.doi.org/10.4064/aa-92-1-89-98

Niederreiter H; Shparlinski IE, 2000, 'On the distribution of pseudorandom numbers and vectors generated by inversive methods', Applicable Algebra in Engineering, Communications and Computing, vol. 10, pp. 189 - 202, http://dx.doi.org/10.1007/s002000050124

Shparlinski IE, 2000, 'Communication complexity and fourier coefficients of the Diffie-Hellman key', Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 1776 LNCS, pp. 259 - 268, http://dx.doi.org/10.1007/10719839_27

Shparlinski IE, 2000, 'Computing Jacobi Symbols modulo Sparse Integers and Polynomials and Some Applications', Journal of Algorithms, vol. 36, pp. 241 - 252, http://dx.doi.org/10.1006/jagm.2000.1091

Shparlinski IE, 2000, 'Linear complexity of the Naor-Reingold pseudo-random function', Information Processing Letters, vol. 76, pp. 95 - 99, http://dx.doi.org/10.1016/S0020-0190(00)00133-2

Shparlinski IE, 2000, 'On the Naor-Reingold pseudo-random function from elliptic curves', Applicable Algebra in Engineering, Communications and Computing, vol. 11, pp. 27 - 34, http://dx.doi.org/10.1007/s002000000023

Von Zur Gathen J; Shparlinski IE, 2000, 'CREW PRAM complexity of modular inversion', SIAM Journal on Computing, vol. 29, pp. 1839 - 1857, http://dx.doi.org/10.1137/S0097539797328070

Canetti R; Friedlander J; Shparlinski I, 1999, 'On certain exponential sums and the distribution of Diffie-Hellman triples', Journal of the London Mathematical Society, vol. 59, pp. 799 - 812, http://dx.doi.org/10.1112/S002461079900736X

Everest GR; Shparlinski IE, 1999, 'Counting the values taken by algebraic exponential polynomials', Proceedings of the American Mathematical Society, vol. 127, pp. 665 - 675, http://dx.doi.org/10.1090/s0002-9939-99-04728-0

Friedlander J; Larsen M; Lieman D; Shparlinski I, 1999, 'On the Correlation of Binary M-sequences', Designs, Codes, and Cryptography, vol. 16, pp. 249 - 256, http://dx.doi.org/10.1023/A:1008383811226

Niederreiter H; Shparlinski IE, 1999, 'On the distribution and lattice structure of nonlinear congruential pseudorandom numbers', Finite Fields and their Applications, vol. 5, pp. 246 - 253, http://dx.doi.org/10.1006/ffta.1999.0257

Von Zur Gathen J; Shparlinski I, 1999, 'Computing components and projections of curves over finite fields', SIAM Journal on Computing, vol. 28, pp. 822 - 840, http://dx.doi.org/10.1137/s009753979427741x

Von Zur Gathen J; Shparlinski I, 1998, 'Orders of Gauss periods in finite fields', Applicable Algebra in Engineering, Communications and Computing, vol. 9, pp. 15 - 24, http://dx.doi.org/10.1007/s002000050093

Everest GR; Shparlinski IE, 1996, 'Divisor sums of generalised exponential polynomials', Canadian Mathematical Bulletin, vol. 39, pp. 35 - 46, http://dx.doi.org/10.4153/CMB-1996-005-5

Karpinski M; Shparlinski I, 1996, 'On some approximation problems concerning sparse polynomials over finite fields', Theoretical Computer Science, vol. 157, pp. 259 - 266, http://dx.doi.org/10.1016/0304-3975(95)00162-X

Shparlinski I, 1996, 'On exponential sums with sparse polynomials and rational functions', Journal of Number Theory, vol. 60, pp. 233 - 244, http://dx.doi.org/10.1006/jnth.1996.0121

Shparlinski I, 1996, 'On finding primitive roots in finite fields', Theoretical Computer Science, vol. 157, pp. 273 - 275, http://dx.doi.org/10.1016/0304-3975(95)00164-6

Shparlinski IE, 1996, 'On irreducible polynomials of small height over finite fields', APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING, vol. 7, pp. 427 - 431, http://dx.doi.org/10.1007/BF01293260

Shparlinski IE, 1996, 'On irreducible polynomials of small height over finite fields', Applicable Algebra in Engineering, Communications and Computing, vol. 7, pp. 427 - 431, http://dx.doi.org/10.1007/BF01293260

Van Der Poorten AJ; Shparlinski IE, 1996, 'On linear recurrence sequences with polynomial coefficients', Glasgow Mathematical Journal, vol. 38, pp. 147 - 155, http://dx.doi.org/10.1017/s0017089500031372

Von Zur Gathen J; Karpinski M; Shparlinski I, 1996, 'Counting curves and their projections', Computational Complexity, vol. 6, pp. 64 - 99, http://dx.doi.org/10.1007/BF01202042

Pappalardi F; Shparlinski I, 1995, 'On artin′s conjecture over function fields', Finite Fields and Their Applications, vol. 1, pp. 399 - 404, http://dx.doi.org/10.1006/ffta.1995.1030

MULLEN GL; SHPARLINSKI I, 1993, 'VALUES OF LINEAR RECURRING SEQUENCES OF VECTORS OVER FINITE-FIELDS', ACTA ARITHMETICA, vol. 65, pp. 221 - 226, http://dx.doi.org/10.4064/aa-65-3-221-226

Shparlinski IE, 1993, 'Finding irreducible and primitive polynomials', Applicable Algebra in Engineering, Communication and Computing, vol. 4, pp. 263 - 268, http://dx.doi.org/10.1007/BF01200150

Shparlinski IE, 1993, 'On bivariate polynomial factorization over finite fields', Mathematics of Computation, vol. 60, pp. 787 - 791, http://dx.doi.org/10.1090/S0025-5718-1993-1176716-3

Shparlinski IE, 1993, 'On parameters of some graphs from finite fields', European Journal of Combinatorics, vol. 14, pp. 589 - 591, http://dx.doi.org/10.1006/eujc.1993.1061

Galiev VI; Polupanov AF; Shparlinski IE, 1992, 'Distances from differences of roots of polynomials to the nearest integers', Information Processing Letters, vol. 43, pp. 143 - 146, http://dx.doi.org/10.1016/0020-0190(92)90006-H

Galiev VI; Polupanov AF; Shparlinski IE, 1992, 'On the construction of solutions of systems of linear ordinary differential equations in the neighbourhood of a regular singularity', Journal of Computational and Applied Mathematics, vol. 39, pp. 151 - 163, http://dx.doi.org/10.1016/0377-0427(92)90126-I

SHPARLINSKI IE, 1992, 'ON GAUSSIAN SUMS FOR FINITE-FIELDS AND ELLIPTIC-CURVES', LECTURE NOTES IN COMPUTER SCIENCE, vol. 573, pp. 5 - 15, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1992KQ18400003&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

SHPARLINSKI IE; TSFASMAN MA; VLADUT SG, 1992, 'CURVES WITH MANY POINTS AND MULTIPLICATION IN FINITE-FIELDS', LECTURE NOTES IN MATHEMATICS, vol. 1518, pp. 145 - 169, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:A1992KR02000014&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Shparlinski IE, 1992, 'A deterministic test for permutation polynomials', Computational Complexity, vol. 2, pp. 129 - 132, http://dx.doi.org/10.1007/BF01202000

Shparlinskiĭ IE, 1992, 'On primitive elements in finite fields and on elliptic curves', Mathematics of the USSR - Sbornik, vol. 71, pp. 41 - 50, http://dx.doi.org/10.1070/SM1992v071n01ABEH001389

Stepanov SA; Shparlinskii IE, 1992, 'An estimate of incomplete multiplicative character sum of polynomials', Discrete Mathematics and Applications, vol. 2, pp. 169 - 174, http://dx.doi.org/10.1515/dma.1992.2.2.169

Van Der Poorten AJ; Shparlinski IE, 1992, 'On the number of zeros of exponential polynomials and related questions', Bulletin of the Australian Mathematical Society, vol. 46, pp. 401 - 412, http://dx.doi.org/10.1017/S0004972700012065

Shparlinskii IE, 1991, 'Estimates of Gaussian sums', Mathematical Notes of the Academy of Sciences of the USSR, vol. 50, pp. 740 - 746, http://dx.doi.org/10.1007/BF01156612

Shparlinskiy IE, 1991, 'On the Distribution of Values of Recurring Sequences and the Bell Numbers in Finite Fields', European Journal of Combinatorics, vol. 12, pp. 81 - 87, http://dx.doi.org/10.1016/S0195-6698(13)80010-8

Perel'muter GI; Shparlinskii IE, 1990, 'The distribution of primitive roots in finite fields', Russian Mathematical Surveys, vol. 45, pp. 223 - 224, http://dx.doi.org/10.1070/RM1990v045n01ABEH002330

Shparlinskii IE, 1990, 'Generalization of Chebyshev polynomials', Siberian Mathematical Journal, vol. 31, pp. 183 - 185, http://dx.doi.org/10.1007/BF00971170

Shparlinskii IE, 1990, 'Some arithmetic properties of recurrence sequences', Mathematical Notes of the Academy of Sciences of the USSR, vol. 47, pp. 612 - 617, http://dx.doi.org/10.1007/BF01170895

Shparlinskiĭ IE; Skorobogatov AN, 1990, 'Exponential sums and rational points on complete intersections', Mathematika, vol. 37, pp. 201 - 208, http://dx.doi.org/10.1112/S0025579300012912

Stepanov SA; Shparlinskii IE, 1990, 'On the construction of a primitive normal basis in a finite field', Mathematics of the USSR - Sbornik, vol. 67, pp. 527 - 533, http://dx.doi.org/10.1070/SM1990v067n02ABEH001369

Shparlinskii IE, 1989, 'Dimension of BCH codes', Problems of information transmission, vol. 25, pp. 77 - 80

Shparlinskii IE, 1989, 'On arithmetical properties of solutions of norm equations', Russian Mathematical Surveys, vol. 44, pp. 216 - 217, http://dx.doi.org/10.1070/RM1989v044n03ABEH002131

Shparlinskii IE, 1989, 'On distribution of values of recurrence sequences', Problems of information transmission, vol. 25, pp. 120 - 125

Shparlinskiĭ IE, 1989, 'On polynomials of prescribed height in finite fields', Mathematics of the USSR - Sbornik, vol. 63, pp. 247 - 255, http://dx.doi.org/10.1070/SM1989v063n01ABEH003271

Shparlinskii IE, 1988, 'Residue classes modulo a prime number in a field of algebraic numbers', Mathematical Notes of the Academy of Sciences of the USSR, vol. 43, pp. 249 - 252, http://dx.doi.org/10.1007/BF01139128

Shparlinskii IE, 1987, 'Number of different prime divisors of recurrence sequences', Mathematical Notes of the Academy of Sciences of the USSR, vol. 42, pp. 773 - 780, http://dx.doi.org/10.1007/BF01138309

Shparlinskii IE, 1986, 'WEIGHT SPECTRA OF SOME CODES.', Problems of information transmission, vol. 22, pp. 111 - 116

Kosachevskaya LL; Romanovtsev VV; Shparlinskii IE, 1985, 'On one sequence of iteration parameters', USSR Computational Mathematics and Mathematical Physics, vol. 25, pp. 89 - 93, http://dx.doi.org/10.1016/0041-5553(85)90046-1

Shparlinskii IE, 1985, 'Coefficients of primitive polynomials', Mathematical Notes of the Academy of Sciences of the USSR, vol. 38, pp. 951 - 954, http://dx.doi.org/10.1007/BF01157011

Shparlinskii IE, 1985, 'Number of prime divisors of recurrence sequences', Mathematical Notes of the Academy of Sciences of the USSR, vol. 38, pp. 529 - 532, http://dx.doi.org/10.1007/BF01137461

Kosachevskaya LL; Shparlinskii IE, 1984, 'The rate of convergence of some iterational processes', USSR Computational Mathematics and Mathematical Physics, vol. 24, pp. 81 - 84, http://dx.doi.org/10.1016/0041-5553(84)90088-0

Shparlinskii IE, 1984, 'Communications of the moscow mathematical society: On the note of convergence of Newton's interpolation process and the power of certain codes', Russian Mathematical Surveys, vol. 39, pp. 199 - 200, http://dx.doi.org/10.1070/RM1984v039n02ABEH003150

Shparlinskii IE, 1984, 'On a multiplicative generator of pseudorandom numbers', USSR Computational Mathematics and Mathematical Physics, vol. 24, pp. 79 - 81, http://dx.doi.org/10.1016/0041-5553(84)90159-9

Kosachevskaya LL; Romanovtsev VV; Shparlinskiy IE, 1983, 'On the spline-based method for experimental data deconvolution', Computer Physics Communications, vol. 29, pp. 227 - 230, http://dx.doi.org/10.1016/0010-4655(83)90002-4

Shparlinskii IE, 1983, 'On one property of a multiplicative transducer of pseudo-random numbers', USSR Computational Mathematics and Mathematical Physics, vol. 23, pp. 158 - 159, http://dx.doi.org/10.1016/S0041-5553(83)80030-5

Kosachevskaya LL; Romanovtsev VV; Shparlinskii IE, 1982, 'On an iterative process for the numerical solution of systems of linear algebraic equations', USSR Computational Mathematics and Mathematical Physics, vol. 22, pp. 232 - 237, http://dx.doi.org/10.1016/0041-5553(82)90114-8

Kosachevskaya LL; Romanovtsev VV; Shparlinskiy IE; Vystavkin AN, 1982, 'New improved algorithm for the iterative solution of a system of linear algebraic equations', Computer Physics Communications, vol. 27, pp. 87 - 89, http://dx.doi.org/10.1016/0010-4655(82)90011-X

Shparlinskii IE, 1981, 'The distribution of the fractional parts of recurrent sequences', USSR Computational Mathematics and Mathematical Physics, vol. 21, pp. 231 - 235, http://dx.doi.org/10.1016/0041-5553(81)90169-5

Levin MB; Shparlinskii IE, 1979, 'The uniform distribution of fractional parts of recurrent sequences', Russian Mathematical Surveys, vol. 34, pp. 207 - 208, http://dx.doi.org/10.1070/RM1979v034n03ABEH003995

Shparlinskii IE, 1979, 'On a completely uniform distribution', USSR Computational Mathematics and Mathematical Physics, vol. 19, pp. 249 - 253, http://dx.doi.org/10.1016/0041-5553(79)90117-4

Shparlinskii IE, 1978, 'Distribution of nonresidues and primitive roots in recurrent sequences', Mathematical Notes of the Academy of Sciences of the USSR, vol. 24, pp. 823 - 828, http://dx.doi.org/10.1007/BF01141537

Chen C; Shparlinski IE, 2021, On a hybrid version of the Vinogradov mean value theorem, http://dx.doi.org10.1007/s10474-020-01111-9, http://arxiv.org/abs/1910.07329v1

Chen C; Shparlinski IE, 2021, Restricted Mean Value Theorems and the Metric Theory of Restricted Weyl Sums, Oxford University Press (OUP), http://dx.doi.org10.1093/qmath/haaa052, http://arxiv.org/abs/1912.01307v2

Banks WD; Shparlinski IE, 2020, Sums with the Möbius function twisted by characters with powerful moduli, American Mathematical Society (AMS), http://dx.doi.org10.1090/tran/7914, http://arxiv.org/abs/1801.10276v1

Kerr B; Shparlinski IE; Yau KH, 2020, A refinement of the burgess bound for character sums, Michigan Mathematical Journal, http://dx.doi.org10.1307/mmj/1573700737, http://arxiv.org/abs/1711.10582v1

Munsch M; Shparlinski IE, 2020, On smooth square-free numbers in arithmetic progressions, http://dx.doi.org10.1112/jlms.12297, http://arxiv.org/abs/1710.04705v3

Dąbrowski A; Pomykała J; Shparlinski IE, 2019, On oracle factoring of integers, http://dx.doi.org, http://arxiv.org/abs/1912.00345v4

Konyagin SV; Makarychev SV; Shparlinski IE; Vyugin IV, 2017, On the new bound for the number of solutions of polynomial equations in subgroups and the structure of graphs of Markoff triples, http://dx.doi.org, http://arxiv.org/abs/1711.05335v2

Mérai L; Shparlinski IE, 2023, Distribution of recursive matrix pseudorandom number generator modulo prime powers, http://arxiv.org/abs/2302.03964v1

Shparlinski IE, 2023, On the number of Diophantine $m$-tuples in finite fields, http://arxiv.org/abs/2301.04063v1

Abdalaoui EHE; Shparlinski IE; Steiner RS, 2022, Chowla and Sarnak Conjectures for Kloosterman Sums, http://arxiv.org/abs/2211.00379v1

Banks W; Shparlinski IE, 2022, On the greatest common divisor of integer parts of polynomials, http://arxiv.org/abs/2205.00253v1

Fouvry É; Shparlinski IE, 2022, On character sums with determinants, http://arxiv.org/abs/2210.15761v1

Hauck M; Shparlinski IE, 2022, Smooth numbers with few digits, http://arxiv.org/abs/2212.10209v1

Kerr B; Shparlinski IE; Wu X; Xi P, 2022, Bounds on bilinear forms with Kloosterman sums, http://arxiv.org/abs/2204.05038v3

Mans B; Sha M; Shparlinski IE; Sutantyo D, 2022, Functional graphs of families of quadratic polynomials, http://arxiv.org/abs/2208.01885v2

Mans B; Sha M; Shparlinski IE; Sutantyo D, 2022, Functional graphs of families of quadratic polynomials, http://dx.doi.org/10.48550/arxiv.2208.01885

Mérai L; Shparlinski IE; Winterhof A, 2022, Character sums over sparse elements of finite fields, http://arxiv.org/abs/2211.08452v1

Ostafe A; Shparlinski IE, 2022, Integer matrices with a given characteristic polynomial and multiplicative dependence of matrices, http://arxiv.org/abs/2203.03880v3

Ostafe A; Shparlinski IE; Voloch JF, 2022, Weil Sums over Small Subgroups, http://arxiv.org/abs/2211.07739v1

Shparlinski IE, 2022, Multiplicative Properties of Hilbert Cubes, http://arxiv.org/abs/2201.00585v2

Bag N; Shparlinski IE, 2021, Bounds on bilinear sums of Kloosterman sums, http://arxiv.org/abs/2111.07311v1

Bagshaw C; Shparlinski IE, 2021, Energy bounds, bilinear sums and their applications in function fields, http://arxiv.org/abs/2112.02257v1

Baker RC; Chen C; Shparlinski IE, 2021, Bounds on the Norms of Maximal Operators on Weyl Sums, http://dx.doi.org/10.48550/arxiv.2107.13674

Baker RC; Chen C; Shparlinski IE, 2021, Large Weyl sums and Hausdorff dimension, http://dx.doi.org/10.48550/arxiv.2108.10439

Baker RC; Munsch M; Shparlinski IE, 2021, Additive energy and a large sieve inequality for sparse sequences, http://dx.doi.org/10.48550/arxiv.2103.12659

Ghioca D; Ostafe A; Saleh S; Shparlinski IE, 2021, On sparsity of representations of polynomials as linear combinations of exponential functions, http://dx.doi.org/10.48550/arxiv.2102.01949

Ghioca D; Shparlinski I, 2021, Order of torsion for reduction of linearly independent points for a family of Drinfeld modules, http://dx.doi.org/10.48550/arxiv.2103.00641

Kaminski M; Shparlinski IE, 2021, 'Sets of Linear Forms Which Are Hard to Compute', in Leibniz International Proceedings in Informatics, LIPIcs, http://dx.doi.org/10.4230/LIPIcs.MFCS.2021.66

Kaminski M; Shparlinski IE; Waldschmidt M, 2021, On sets of linear forms of maximal complexity, http://dx.doi.org/10.1007/s00037-022-00234-5

Kerr B; Shkredov ID; Shparlinski IE; Zaharescu A, 2021, Energy bounds for modular roots and their applications, http://dx.doi.org/10.48550/arxiv.2103.09405

Ostafe A; Shparlinski IE, 2021, Additive energy of cyclic matrix groups and character sums with matrix exponential functions, http://dx.doi.org/10.48550/arxiv.2108.13146

Ostafe A; Shparlinski IE; Voloch JF, 2021, Equations and character sums with matrix powers, Kloosterman sums over small subgroups and quantum ergodicity, http://arxiv.org/abs/2110.10941v1

Shparlinski IE, 2021, On the Glasner property for matrices with polynomial entries, http://arxiv.org/abs/2111.05644v1

Shparlinski IE; Thuswaldner JM, 2021, Weyl sums over integers with digital restrictions, http://dx.doi.org/10.48550/arxiv.2105.04835

Banks W; Shparlinski I, 2020, On a conjecture of Soundararajan, http://dx.doi.org/10.48550/arxiv.2009.06800

Brandes J; Shparlinski IE, 2020, Two-dimensional Weyl sums failing square-root cancellation along lines, http://dx.doi.org/10.48550/arxiv.2012.08877

Chen C; Shparlinski IE, 2020, Hybrid bounds on two-parametric family Weyl sums along smooth curves, http://dx.doi.org/10.48550/arxiv.2003.02419

Ghioca D; Ostafe A; Saleh S; Shparlinski IE, 2020, A sparsity result for the Dynamical Mordell-Lang Conjecture in positive characteristic, http://dx.doi.org/10.48550/arxiv.2012.13711

Karpinski M; Shparlinski I, 2020, Noisy polynomial interpolation modulo prime powers, http://dx.doi.org/10.48550/arxiv.2006.05685

Kerr B; Mello J; Shparlinski I, 2020, An effective local-global principle for algebraic varieties and the sum product problem in finite fields, http://dx.doi.org/10.48550/arxiv.2005.02923

Kerr B; Mello J; Shparlinski IE, 2020, On elements of large order of elliptic curves and multiplicative dependent images of rational functions over finite fields, http://dx.doi.org/10.48550/arxiv.2008.00433

Kerr B; Mérai L; Shparlinski IE, 2020, On digits of Mersenne numbers, http://dx.doi.org/10.48550/arxiv.2001.03380

Konyagin SV; Shparlinski IE; Vyugin IV, 2020, Polynomial Equations in Subgroups and Applications, http://dx.doi.org/10.48550/arxiv.2005.05315

Li R; Shparlinski IE, 2020, Effective bounds on multiplicatively dependent orbits of integer polynomials modulo S-integers, http://dx.doi.org/10.48550/arxiv.2001.09721

Macourt S; Petridis G; Shkredov ID; Shparlinski IE, 2020, Bounds of Trilinear and Trinomial Exponential Sums, http://dx.doi.org/10.48550/arxiv.2003.03493

Mérai L; Shparlinski IE, 2020, On the Dynamical System Generated by the Möbius transformation at Prime Times, http://dx.doi.org/10.48550/arxiv.2009.01089

Ostafe A; Shparlinski I, 2020, On the Skolem problem and some related questions for parametric families of linear recurrence sequences, http://dx.doi.org/10.48550/arxiv.2005.06713

Shkredov ID; Shparlinski IE; Zaharescu A, 2020, On the distribution of modular square roots of primes, http://dx.doi.org/10.48550/arxiv.2009.03460

Shparlinski IE; Wang Q, 2020, Exponential sums with sparse polynomials over finite fields, http://dx.doi.org/10.48550/arxiv.2007.14551

di Benedetto D; Garaev MZ; García VC; González-Sánchez D; Shparlinski IE; Trujillo CA, 2020, New estimates for exponential sums over multiplicative subgroups and intervals in prime fields, http://dx.doi.org/10.48550/arxiv.2003.06165

Banks W; Shparlinski I, 2019, Congruences with intervals and arbitrary sets, http://dx.doi.org/10.48550/arxiv.1907.03943