Dr Alina Ostafe
Senior Lecturer

Dr Alina Ostafe

Science
School of Mathematics & Statistics
Phone
93857058
Location
School of Mathematics and Statistics University of New South Wales Sydney NSW 2052 The Red Centre Room 5104
  • Books | 2014
    Niederreiter H; Ostafe A; Panario D; Winterhof A, 2014, Algebraic Curves and Finite Fields Introduction, Niederreiter H; Ostafe A; Panario D; Winterhof A, (eds.), Radon Series on Computational and Applied Mathematics, WALTER DE GRUYTER GMBH, http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000352560600001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1
  • Book Chapters | 2017
    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
    Book Chapters | 2016
    Ostafe A; Sha M, 2016, 'Counting dynamical systems over finite fields', in Contemporary Mathematics, pp. 187 - 203, http://dx.doi.org/10.1090/conm/669/13429
    Book Chapters | 2013
    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
    Book Chapters | 2013
    Ostafe A; Winterhof A, 2013, 'Some applications of character sums.', in Mullen GL; Panario D (ed.), Handbook of Finite Fields, CRC Press, pp. 170 - 184, https://www.crcpress.com/product/isbn/9781439873786
  • Edited Books | 2014
    Niederreiter H; Ostafe A; Panario D; Winterhof A, (eds.), 2014, Algebraic Curves and Finite Fields, WALTER DE GRUYTER GMBH, https://www.degruyter.com/view/product/207742
  • 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, 2022, 'On a problem of Lang for matrix polynomials', Bulletin of the London Mathematical Society, http://dx.doi.org/10.1112/blms.12642
    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 | 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
    Journal articles | 2021
    Bérczes A; Mello J; Ostafe A; Sha M, 2021, 'Multiplicative dependence of rational values modulo approximate finitely generated groups', , http://arxiv.org/abs/2107.05371v1
    Journal articles | 2021
    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
    Journal articles | 2021
    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
    Journal articles | 2021
    Ostafe A, 2021, 'On a Problem of Lang for Matrix Polynomials', , http://arxiv.org/abs/2105.07705v2
    Journal articles | 2021
    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, http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000669490500001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1
    Journal articles | 2021
    Ostafe A; Shparlinski IE, 2021, 'Additive energy of cyclic matrix groups and character sums with matrix exponential functions', , http://arxiv.org/abs/2108.13146v2
    Journal articles | 2021
    Ostafe A; Shparlinski IE, 2021, 'On the Skolem problem and some related questions for parametric families of linear recurrence sequences', Canadian Journal of Mathematics, pp. 1 - 20, http://dx.doi.org/10.4153/S0008414X21000080
    Journal articles | 2020
    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, 2019, 'Polynomial values in affine subspaces of finite fields', Journal d'Analyse Mathematique, vol. 138, pp. 49 - 81, http://dx.doi.org/10.1007/s11854-019-0021-y
    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, vol. 00, http://dx.doi.org/10.1090/tran/7974
    Journal articles | 2018
    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
    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, vol. 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, vol. 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, vol. 50, pp. 35 - 65, http://dx.doi.org/10.1016/j.ffa.2017.11.002
    Journal articles | 2018
    Ostafe A, 2018, 'On Some Extensions of the Ailon–Rudnick Theorem', Monatshefte für Mathematik, vol. 181, pp. 451 - 471, http://dx.doi.org/10.1007/s00605-016-0911-3
    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, vol. 669, pp. 187 - 203, http://dx.doi.org/10.1090/conm/669
    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, vol. 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, vol. 5, https://arxiv.org/abs/1706.05874
    Journal articles | 2016
    Gomez-Perez D; Gutierrez J; Ostafe A, 2016, 'Common composites of triangular polynomial systems and hash functions', JOURNAL OF SYMBOLIC COMPUTATION, vol. 72, pp. 182 - 195, http://dx.doi.org/10.1016/j.jsc.2015.02.005
    Journal articles | 2016
    Ostafe A, 2016, 'On roots of unity in orbits of rational functions', Proceedings of the American Mathematical Society, vol. 145, pp. 1927 - 1936, http://dx.doi.org/10.1090/proc/13433
    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, vol. 164, pp. 433 - 437, http://dx.doi.org/10.1016/j.jnt.2016.01.014
    Journal articles | 2015
    Ostafe A; Sha M, 2015, 'On the quantitative dynamical Mordell-Lang conjecture', Journal of Number Theory, vol. 156, pp. 161 - 182, http://dx.doi.org/10.1016/j.jnt.2015.04.011
    Journal articles | 2014
    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
    Journal articles | 2014
    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
    Journal articles | 2014
    Gómez-Pérez D; Ostafe A; Topuzoǧlu A, 2014, 'On the Carlitz rank of permutations ofFqand pseudorandom sequences', Journal of Complexity, vol. 30, pp. 279 - 289, http://dx.doi.org/10.1016/j.jco.2013.11.001
    Journal articles | 2012
    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
    Journal articles | 2012
    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
    Journal articles | 2012
    Ostafe A, 2012, 'Pseudorandom vector sequences of maximal period generated by triangular polynomial dynamical systems', Designs, Codes, and Cryptography, vol. 63, pp. 59 - 72, http://dx.doi.org/10.1007/s10623-011-9535-8
    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, vol. 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, vol. 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, vol. 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, vol. 28, pp. 238 - 249, http://dx.doi.org/10.1016/j.jco.2011.10.010
    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, vol. abs/1102.1053
    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 | 2011
    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
    Journal articles | 2011
    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
    Journal articles | 2011
    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
    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, vol. 7, pp. 1557 - 1571, http://dx.doi.org/10.1142/S1793042111004484
    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), vol. 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, vol. 23, pp. 501 - 513, http://dx.doi.org/10.1007/s13163-010-0029-4
    Journal articles | 2010
    Ostafe A, 2010, 'Multivariate permutation polynomial systems and nonlinear pseudorandom number generators', Finite Fields and their Applications, vol. 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), vol. 6087 LNCS, pp. 62 - 72, http://dx.doi.org/10.1007/978-3-642-13797-6_5
    Journal articles | 2010
    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
    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, vol. 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, vol. 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, vol. 2, pp. 49 - 67, http://dx.doi.org/10.1007/s12095-009-0016-0
    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, vol. 4, pp. 369 - 379, http://dx.doi.org/10.3934/amc.2010.4.369
  • 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
    Preprints | 2022
    Ostafe A; Shparlinski IE, 2022, Integer matrices with a given characteristic polynomial and multiplicative dependence of matrices, http://arxiv.org/abs/2203.03880v2
    Preprints | 2021
    Bérczes A; Mello J; Ostafe A; Sha M, 2021, Multiplicative dependence of rational values modulo approximate finitely generated groups
    Preprints | 2021
    Ghioca D; Ostafe A; Saleh S; Shparlinski IE, 2021, On sparsity of representations of polynomials as linear combinations of exponential functions
    Preprints | 2021
    Ostafe A; Shparlinski IE, 2021, Additive energy of cyclic matrix groups and character sums with matrix exponential functions
    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
    Preprints | 2020
    Barroero F; Capuano L; Mérai L; Ostafe A; Sha M, 2020, Multiplicative and linear dependence in finite fields and on elliptic curves modulo primes
    Preprints | 2020
    Ghioca D; Ostafe A; Saleh S; Shparlinski IE, 2020, A sparsity result for the Dynamical Mordell-Lang Conjecture in positive characteristic
    Preprints | 2020
    Ostafe A; Shparlinski I, 2020, On the Skolem problem and some related questions for parametric families of linear recurrence sequences
    Preprints | 2019
    Dietmann R; Ostafe A; Shparlinski IE, 2019, Discriminants of Fields Generated by Polynomials of Given Height
    Preprints | 2019
    Mérai L; Ostafe A; Shparlinski IE, 2019, Dynamical irreducibility of polynomials modulo primes
    Preprints | 2019
    Ostafe A; Pottmeyer L; Shparlinski IE, 2019, Perfect powers in value sets and orbits of polynomials
    Preprints | 2018
    Bérczes A; Ostafe A; Shparlinski IE; Silverman JH, 2018, Multiplicative dependence among iterated values of rational functions modulo finitely generated groups
    Preprints | 2017
    Chang M-C; D'Andrea C; Ostafe A; Shparlinski IE; Sombra M, 2017, Orbits of Polynomial Dynamical Systems Modulo Primes
    Preprints | 2017
    Ostafe A; Sha M; Shparlinski IE; Zannier U, 2017, On abelian multiplicatively dependent points on a curve in a torus
    Preprints | 2017
    Ostafe A; Sha M; Shparlinski IE; Zannier U, 2017, On multiplicative dependence of values of rational functions and a generalisation of the Northcott theorem
    Preprints | 2015
    D'Andrea C; Ostafe A; Shparlinski IE; Sombra M, 2015, Reductions Modulo Primes of Systems of Polynomial Equations and Algebraic Dynamical Systems
    Preprints | 2015
    Gómez-Pérez D; Ostafe A; Sha M, 2015, The Arithmetic of Consecutive Polynomial Sequences over Finite Fields
    Preprints | 2015
    Ostafe A; Sha M, 2015, Counting dynamical systems over finite fields
    Preprints | 2015
    Ostafe A; Sha M, 2015, On the quantitative dynamical Mordell-Lang conjecture
    Preprints | 2012
    Gomez-Perez D; Nicolas AP; Ostafe A; Sadornil D, 2012, Stable Polynomials over Finite Fields
    Preprints | 2011
    Blackburn SR; Ostafe A; Shparlinski IE, 2011, On the Distribution of the Subset Sum Pseudorandom Number Generator on Elliptic Curves
    Preprints | 2011
    Ostafe A; Shparlinski I, 2011, Degree Growth, Linear Independence and Periods of a Class of Rational Dynamical Systems
    Conference Papers | 2011
    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, Ghent, BELGIUM, pp. 153 - +, presented at 10th International Conference on Finite Fields and Their Applications, Ghent, BELGIUM, 11 July 2011 - 15 July 2011, http://dx.doi.org/10.1090/conm/579/11527
    Preprints | 2010
    Ostafe A; Shparlinski IE, 2010, Pseudorandomness and Dynamics of Fermat Quotients
    Preprints | 2009
    Ferguson R; Hoffman C; Luca F; Ostafe A; Shparlinski I, 2009, Some Additive Combinatorics Problems in Matrix Rings
    Preprints | 2009
    Ostafe A; Shparlinski I, 2009, On the Degree Growth in Some Polynomial Dynamical Systems and Nonlinear Pseudorandom Number Generators
    Preprints | 2009
    Ostafe A; Shparlinski IE, 2009, On the Length of Critical Orbits of Stable Quadratic Polynomials
    Preprints | 2009
    Ostafe A; Shparlinski IE, 2009, Pseudorandom Numbers and Hash Functions from Iterations of Multivariate Polynomials