By Associate Professor Alina Ostafe

Journal articles

Kurlberg P; Ostafe A; Rudnick Z; Shparlinski IE, 2025, 'On Quantum Ergodicity for Higher Dimensional Cat Maps', Communications in Mathematical Physics, 406, http://dx.doi.org/10.1007/s00220-025-05350-1

Afifurrahman M; Kuperberg V; Ostafe A; Shparlinski IE, 2025, 'Statistics of ranks, determinants and characteristic polynomials of rational matrices', Forum Mathematicum, 37, pp. 1259 - 1289, http://dx.doi.org/10.1515/forum-2024-0114

Bérczes A; Bugeaud Y; Gyory K; Mello J; Ostafe A; Sha M, 2025, 'Explicit bounds for the solutions of superelliptic equations over number fields', Forum Mathematicum, 37, pp. 135 - 158, http://dx.doi.org/10.1515/forum-2023-0381

Bérczes A; Hajdu L; Ostafe A; Shparlinski IE, 2025, 'Multiplicative dependence in linear recurrence sequences', Canadian Mathematical Bulletin, http://dx.doi.org/10.4153/S0008439525000475

Mohammadi A; Ostafe A; Shparlinski IE, 2024, 'On some matrix counting problems', Journal of the London Mathematical Society, 110, http://dx.doi.org/10.1112/jlms.70044

Bérczes A; Bugeaud Y; Győry K; Mello J; Ostafe A; Sha M, 2024, 'Multiplicative dependence of rational values modulo approximate finitely generated groups', Mathematical Proceedings of the Cambridge Philosophical Society, 177, pp. 149 - 165, http://dx.doi.org/10.1017/S0305004124000173

Dietmann R; Ostafe A; Shparlinski IE, 2024, 'Discriminants of fields generated by polynomials of given height', Israel Journal of Mathematics, 260, pp. 73 - 103, http://dx.doi.org/10.1007/s11856-023-2557-x

Bulinski K; Ostafe A; Shparlinski I, 2024, 'Counting embeddings of free groups into $\mathrm{SL}_2(\mathbb{Z})$ and its subgroups', ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE, pp. 12, http://dx.doi.org/10.2422/2036-2145.202307_011

Ferraguti A; Ostafe A; Zannier U, 2024, 'Cyclotomic and abelian points in backward orbits of rational functions', Advances in Mathematics, 438, pp. 109463, http://dx.doi.org/10.1016/j.aim.2023.109463

Ostafe A; Shparlinski IE; Voloch JF, 2024, 'Weil Sums over Small Subgroups', Mathematical Proceedings of the Cambridge Philosophical Society, 176, pp. 39 - 53, http://dx.doi.org/10.1017/S0305004123000415

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

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

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

Ostafe A; Shparlinski IE; Pottmeyer L, 2022, 'Perfect powers in value sets and orbits of polynomials', The New York Journal of Mathematics, 27, pp. 903 - 917

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

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, 105, pp. 2076 - 2103, http://dx.doi.org/10.1112/jlms.12554

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

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

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, 2022, pp. 16094 - 16137, http://dx.doi.org/10.1093/imrn/rnab171

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

Ostafe A, 2019, 'Polynomial values in affine subspaces of finite fields', Journal d'Analyse Mathematique, 138, pp. 49 - 81, http://dx.doi.org/10.1007/s11854-019-0021-y

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

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, http://dx.doi.org/10.1307/mmj/1556589745

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

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, http://dx.doi.org/10.1093/qmath/hax045

Ostafe A, 2018, 'On Some Extensions of the Ailon–Rudnick Theorem', Monatshefte für Mathematik, 181, pp. 451 - 471, http://dx.doi.org/10.1007/s00605-016-0911-3

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

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

Ostafe A, 2016, 'On roots of unity in orbits of rational functions', Proceedings of the American Mathematical Society, http://dx.doi.org/10.1090/proc/13433

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

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

Ostafe A; Sha M, 2015, 'On the quantitative dynamical Mordell-Lang conjecture', Journal of Number Theory, 156, pp. 161 - 182, http://dx.doi.org/10.1016/j.jnt.2015.04.011

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

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

Gómez-Pérez D; Ostafe A; Topuzoǧlu A, 2014, 'On the Carlitz rank of permutations of^Fqand 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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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