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
Ostafe A, 2013, 'Iterations of Rational Functions: Some Algebraic and Arithmetic Aspects', in Finite Fields and Their Applications, DE GRUYTER, pp. 197 - 232, http://dx.doi.org/10.1515/9783110283600.197
Ostafe A; Shparlinski IE; Voloch JF, 2023, 'Equations and Character Sums with Matrix Powers, Kloosterman Sums over Small Subgroups, and Quantum Ergodicity', International Mathematics Research Notices, 2023, pp. 14196 - 14238, http://dx.doi.org/10.1093/imrn/rnac226
Journal articles | 2023
Ostafe A, 2023, 'Corrigendum to: On a problem of Lang for matrix polynomials (Bulletin of the London Mathematical Society, (2022), 54, 5, (1552-1567), 10.1112/blms.12642)', Bulletin of the London Mathematical Society, 55, pp. 2086, http://dx.doi.org/10.1112/blms.12874
Journal articles | 2023
Ostafe ALINA; Shparlinski IE; Voloch JF, 2023, 'Weil Sums over Small Subgroups', Mathematical Proceedings of the Cambridge Philosophical Society, pp. 1 - 15, http://dx.doi.org/10.1017/S0305004123000415
Journal articles | 2022
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
Journal articles | 2022
Ostafe A; Shparlinski IE; Pottmeyer L, 2022, 'Perfect powers in value sets and orbits of polynomials', The New York Journal of Mathematics
Journal articles | 2022
Ostafe A; Shparlinski IE, 2022, 'On the Skolem problem and some related questions for parametric families of linear recurrence sequences', Canadian Journal of Mathematics, 74, pp. 773 - 792, http://dx.doi.org/10.4153/S0008414X21000080
Journal articles | 2022
Ostafe A, 2022, 'On a problem of Lang for matrix polynomials', Bulletin of the London Mathematical Society, 54, pp. 1552 - 1567, http://dx.doi.org/10.1112/blms.12642
Journal articles | 2021
Barroero F; Capuano L; Merai L; Ostafe A; Sha M, 2021, 'Multiplicative and Linear Dependence in Finite Fields and on Elliptic Curves Modulo Primes', International Mathematics Research Notices, http://dx.doi.org/10.1093/imrn/rnab171
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, 104, pp. 381 - 390, http://dx.doi.org/10.1017/S0004972721000083
Ostafe A; Shparlinski IE, 2021, 'Additive energy of cyclic matrix groups and character sums with matrix
exponential functions', , http://arxiv.org/abs/2108.13146v2
Barroero F; Capuano L; Mérai L; Ostafe A; Sha M, 2020, 'Multiplicative and linear dependence in finite fields and on elliptic
curves modulo primes', , http://arxiv.org/abs/2008.00389v2
Journal articles | 2019
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
Journal articles | 2019
Dietmann R; Ostafe A; Shparlinski IE, 2019, 'Discriminants of Fields Generated by Polynomials of Given Height', , http://arxiv.org/abs/1909.00135v2
Journal articles | 2019
Ostafe A; Young M, 2019, 'On algebraic integers of bounded house and preperiodicity in polynomial
semigroup dynamics', Transactions of the American Mathematical Society, 00, http://dx.doi.org/10.1090/tran/7974
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, 146, pp. 2015 - 2025, http://dx.doi.org/10.1090/proc/13904
Journal articles | 2018
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, 371, pp. 1169 - 1198, http://dx.doi.org/10.1090/tran/7437
Journal articles | 2018
Gómez-Pérez D; Nicolás AP; Ostafe A; Sadornil D, 2018, 'Stable polynomials over finite fields', Revista Matematica Iberoamericana, 30, pp. 523 - 535, http://dx.doi.org/10.4171/rmi/791
Journal articles | 2018
Gómez-Pérez D; Ostafe A; Sha M, 2018, 'The Arithmetic of Consecutive Polynomial Sequences over Finite Fields', Finite Fields and Their Applications, 50, pp. 35 - 65, http://dx.doi.org/10.1016/j.ffa.2017.11.002
Journal articles | 2018
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, 69, pp. 391 - 401, http://dx.doi.org/10.1093/qmath/hax045
Journal articles | 2018
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, 5, https://arxiv.org/abs/1706.05874
Journal articles | 2018
Ostafe A; Sha M, 2018, 'Counting Dynamical Systems over Finite Fields', Contemporary Mathematics, pp. 187 - 203, http://dx.doi.org/10.1090/conm/669
Journal articles | 2018
Ostafe A; Sha M, 2018, 'Counting dynamical systems over finite fields', Contemporary Mathematics, 669, pp. 187 - 203, http://dx.doi.org/10.1090/conm/669
Gomez-Perez D; Gutierrez J; Ostafe A, 2016, 'Common composites of triangular polynomial systems and hash functions', JOURNAL OF SYMBOLIC COMPUTATION, 72, pp. 182 - 195, http://dx.doi.org/10.1016/j.jsc.2015.02.005
Journal articles | 2016
Ostafe A; Sha M, 2016, 'Corrigendum to On the quantitative dynamical Mordell-Lang conjecture [J. Number Theory, 156, (2015), 161-182] DOI: 10.1016/j.jnt.2015.04.011', Journal of Number Theory, 164, pp. 433 - 437, http://dx.doi.org/10.1016/j.jnt.2016.01.014
Journal articles | 2016
Ostafe A, 2016, 'On roots of unity in orbits of rational functions', Proceedings of the American Mathematical Society, 145, pp. 1927 - 1936, http://dx.doi.org/10.1090/proc/13433
Gómez-Pérez D; Ostafe A; Shparlinski I, 2014, 'Algebraic entropy, automorphisms and sparsity of algebraic dynamical systems and pseudorandom number generators', Mathematics of Computation, 83, pp. 1535 - 1550, http://dx.doi.org/10.1090/S0025-5718-2013-02780-9
Journal articles | 2014
Gómez-Pérez D; Ostafe A; Shparlinski IE, 2014, 'On irreducible divisors of iterated polynomials', Revista Matematica Iberoamericana, 30, pp. 1123 - 1134, http://dx.doi.org/10.4171/rmi/809
Journal articles | 2014
Gómez-Pérez D; Ostafe A; Topuzoǧlu A, 2014, 'On the Carlitz rank of permutations ofFqand pseudorandom sequences', Journal of Complexity, 30, pp. 279 - 289, http://dx.doi.org/10.1016/j.jco.2013.11.001
Cilleruelo J; Garaev MZ; Ostafe A; Shparlinski IE, 2012, 'On the concentration of points of polynomial maps and applications', Mathematische Zeitschrift, 272, pp. 825 - 837, http://dx.doi.org/10.1007/s00209-011-0959-7
Journal articles | 2012
Ostafe A; Shparlinski I, 2012, 'Degree growth, linear independence and periods of a class of rational dynamical systems', ARITHMETIC, GEOMETRY, CRYPTOGRAPHY AND CODING THEORY, 574, pp. 131 - 143, http://dx.doi.org/10.1090/conm/574/11426
Journal articles | 2012
Ostafe A; Shparlinski IE, 2012, 'Exponential sums over points of elliptic curves with reciprocals of primes', Mathematika, 58, pp. 21 - 33, http://dx.doi.org/10.1112/S0025579311001719
Journal articles | 2012
Ostafe A; Shparlinski IE, 2012, 'Multiplicative character sums and products of sparse integers in residue classes', Periodica Mathematica Hungarica, 64, pp. 247 - 255, http://dx.doi.org/10.1007/s10998-012-6771-2
Journal articles | 2012
Ostafe A; Shparlinski IE, 2012, 'On the power generator and its multivariate analogue', Journal of Complexity, 28, pp. 238 - 249, http://dx.doi.org/10.1016/j.jco.2011.10.010
Journal articles | 2012
Ostafe A, 2012, 'Pseudorandom vector sequences of maximal period generated by triangular polynomial dynamical systems', Designs, Codes, and Cryptography, 63, pp. 59 - 72, http://dx.doi.org/10.1007/s10623-011-9535-8
Journal articles | 2011
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
Journal articles | 2011
Blackburn SR; Ostafe A; Shparlinski IE, 2011, 'On the Distribution of the Subset Sum Pseudorandom Number Generator on Elliptic Curves', CoRR, abs/1102.1053
Journal articles | 2011
Ostafe A; Shparlinski IE; Winterhof A, 2011, 'Multiplicative character sums of a class of nonlinear recurrence vector sequences', International Journal of Number Theory, 7, pp. 1557 - 1571, http://dx.doi.org/10.1142/S1793042111004484
Journal articles | 2011
Ostafe A; Shparlinski IE, 2011, 'On the waring problem with Dickson polynomials in finite fields', Proceedings of the American Mathematical Society, 139, pp. 3815 - 3820, http://dx.doi.org/10.1090/S0002-9939-2011-10843-8
Journal articles | 2011
Ostafe A; Shparlinski IE, 2011, 'Pseudorandomness and dynamics of fermat quotients*', SIAM Journal on Discrete Mathematics, 25, pp. 50 - 71, http://dx.doi.org/10.1137/100798466
Journal articles | 2011
Ostafe A; Shparlinski IE, 2011, 'Twisted exponential sums over points of elliptic curves', Acta Arithmetica, 148, pp. 77 - 92, http://dx.doi.org/10.4064/aa148-1-6
Journal articles | 2011
Ostafe A, 2011, 'Pseudorandom vector sequences of maximal period generated by triangular polynomial dynamical systems', Designs, Codes, and Cryptography, pp. 1 - 14, http://dx.doi.org/10.1007/s10623-011-9535-8
Journal articles | 2010
Chen Z; Ostafe A; Winterhof A, 2010, 'Structure of pseudorandom numbers derived from fermat quotients', Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 6087 LNCS, pp. 73 - 85, http://dx.doi.org/10.1007/978-3-642-13797-6_6
Journal articles | 2010
Ferguson R; Hoffman C; Luca F; Ostafe A; Shparlinski IE, 2010, 'Some additive combinatorics problems in matrix rings', Revista Matematica Complutense, 23, pp. 501 - 513, http://dx.doi.org/10.1007/s13163-010-0029-4
Journal articles | 2010
Ostafe A; Pelican E; Shparlinski IE, 2010, 'On pseudorandom numbers from multivariate polynomial systems', Finite Fields and their Applications, 16, pp. 320 - 328, http://dx.doi.org/10.1016/j.ffa.2010.05.002
Journal articles | 2010
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, 4, pp. 369 - 379, http://dx.doi.org/10.3934/amc.2010.4.369
Journal articles | 2010
Ostafe A; Shparlinski IE, 2010, 'On the degree growth in some polynomial dynamical systems and nonlinear pseudorandom number generators', Mathematics of Computation, 79, pp. 501 - 511, http://dx.doi.org/10.1090/S0025-5718-09-02271-6
Journal articles | 2010
Ostafe A; Shparlinski IE, 2010, 'On the length of critical orbits of stable quadratic polynomials', Proceedings of the American Mathematical Society, 138, pp. 2653 - 2656, http://dx.doi.org/10.1090/S0002-9939-10-10404-3
Journal articles | 2010
Ostafe A; Shparlinski IE, 2010, 'Pseudorandom numbers and hash functions from iterations of multivariate polynomials', Cryptography and Communications, 2, pp. 49 - 67, http://dx.doi.org/10.1007/s12095-009-0016-0
Journal articles | 2010
Ostafe A, 2010, 'Multivariate permutation polynomial systems and nonlinear pseudorandom number generators', Finite Fields and their Applications, 16, pp. 144 - 154, http://dx.doi.org/10.1016/j.ffa.2009.12.003
Journal articles | 2010
Ostafe A, 2010, 'Pseudorandom vector sequences derived from triangular polynomial systems with constant multipliers', Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 6087 LNCS, pp. 62 - 72, http://dx.doi.org/10.1007/978-3-642-13797-6_5
Preprints | 2022
Ferraguti A; Ostafe A; Zannier U, 2022, Cyclotomic and abelian points in backward orbits of rational functions, , http://arxiv.org/abs/2203.10034v1
Ostafe A; Shparlinski IE, 2022, Integer matrices with a given characteristic polynomial and
multiplicative dependence of matrices, , http://arxiv.org/abs/2203.03880v4
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
Preprints | 2021
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
Barroero F; Capuano L; Mérai L; Ostafe A; Sha M, 2020, Multiplicative and linear dependence in finite fields and on elliptic curves modulo primes, , http://dx.doi.org/10.48550/arxiv.2008.00389
Preprints | 2020
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
Preprints | 2020
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
Ostafe A; Sha M; Shparlinski IE; Zannier U, 2017, On multiplicative dependence of values of rational functions and a generalisation of the Northcott theorem, , http://dx.doi.org/10.48550/arxiv.1706.05874
Preprints | 2015
D'Andrea C; Ostafe A; Shparlinski IE; Sombra M, 2015, Reductions Modulo Primes of Systems of Polynomial Equations and Algebraic Dynamical Systems, , http://dx.doi.org/10.48550/arxiv.1505.05814
Blackburn SR; Ostafe A; Shparlinski IE, 2011, On the Distribution of the Subset Sum Pseudorandom Number Generator on Elliptic Curves, , http://dx.doi.org/10.48550/arxiv.1102.1053
Ostafe A; Thomson D; Winterhof A, 2011, 'On the Waring Problem with multivariate Dickson polynomials', in Lavrauw M; Mullen GL; Nikova S; Panario D; Storme L(eds.), THEORY AND APPLICATIONS OF FINITE FIELDS, AMER MATHEMATICAL SOC, BELGIUM, Ghent, pp. 153 - +, presented at 10th International Conference on Finite Fields and Their Applications, BELGIUM, Ghent, 11 July 2011 - 15 July 2011, http://dx.doi.org/10.1090/conm/579/11527
Ostafe A; Shparlinski I, 2009, On the Degree Growth in Some Polynomial Dynamical Systems and Nonlinear Pseudorandom Number Generators, , http://dx.doi.org/10.48550/arxiv.0902.3884