By Associate Professor Alina Ostafe

Preprints

Ostafe A; Shparlinski IE, 2026, Counting Irreducible polynomials with coefficients from thin subgroups, http://dx.doi.org/10.48550/arxiv.2601.12968

Ostafe A; Shparlinski IE, 2026, Counting integer matrices with square-free determinants, http://dx.doi.org/10.48550/arxiv.2503.13768

Ostafe A; Shparlinski IE, 2026, On the sparsity of non-diagonalisable integer matrices and matrices with a given discriminant, http://dx.doi.org/10.48550/arxiv.2312.12626

Afifurrahman M; Kuperberg V; Ostafe A; Shparlinski IE, 2026, Statistics of ranks, determinants and characteristic polynomials of rational matrices, http://dx.doi.org/10.48550/arxiv.2401.10086

Bérczes A; Bhakta S; Hajdu L; Ostafe A; Shparlinski IE, 2025, Multiplicative dependence in the denominators of points of elliptic curves, http://dx.doi.org/10.48550/arxiv.2510.05462

Kurlberg P; Ostafe A; Rudnick Z; Shparlinski IE, 2025, On quantum ergodicity for higher dimensional cat maps, http://dx.doi.org/10.48550/arxiv.2411.05997

Ostafe A; Pomerance C; Shparlinski IE, 2025, Counting solvable $\mathcal S$-unit equations and linear recurrence sequences with zeros, http://dx.doi.org/10.48550/arxiv.2503.03985

Manning A; Ostafe A; Shparlinski IE, 2025, Counting matrices over finite rank multiplicative groups, http://dx.doi.org/10.48550/arxiv.2502.07100

Bérczes A; Hajdu L; Ostafe A; Shparlinski IE, 2025, Multiplicative dependence in linear recurrence sequences, http://dx.doi.org/10.48550/arxiv.2501.17365

Habegger P; Ostafe A; Shparlinski IE, 2024, Integer matrices with a given characteristic polynomial and multiplicative dependence of matrices, http://dx.doi.org/10.48550/arxiv.2203.03880

Ostafe A; Shparlinski IE, 2024, On the frequency of primes preserving dynamical irreducibility of polynomials, http://dx.doi.org/10.48550/arxiv.2407.20464

Ferraguti A; Ostafe A; Zannier U, 2023, Cyclotomic and abelian points in backward orbits of rational functions, http://dx.doi.org/10.48550/arxiv.2203.10034

Mohammadi A; Ostafe A; Shparlinski I, 2023, On some matrix counting problems, http://dx.doi.org/10.48550/arxiv.2310.05038

Bérczes A; Bugeaud Y; Győry K; Mello J; Ostafe A; Sha M, 2023, Explicit bounds for the solutions of superelliptic equations over number fields, http://dx.doi.org/10.48550/arxiv.2310.09704

Bulinski K; Ostafe A; Shparlinski IE, 2023, Counting embeddings of free groups into $\mathrm{SL}_2(\mathbb{Z})$ and its subgroups, http://dx.doi.org/10.48550/arxiv.2304.10980

Ostafe A; Shparlinski IE; Voloch JF, 2022, Weil Sums over Small Subgroups, http://dx.doi.org/10.48550/arxiv.2211.07739

Dietmann R; Ostafe A; Shparlinski IE, 2021, Discriminants of Fields Generated by Polynomials of Given Height, http://dx.doi.org/10.48550/arxiv.1909.00135

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://dx.doi.org/10.48550/arxiv.2110.10941

Bérczes A; Bugeaud Y; Győry K; Mello J; Ostafe A; Sha M, 2021, Multiplicative dependence of rational values modulo approximate finitely generated groups

Ostafe A; Shparlinski I, 2021, On the Skolem problem and some related questions for parametric families of linear recurrence sequences, http://dx.doi.org/10.48550/arxiv.2005.06713

Barroero F; Capuano L; Mérai L; Ostafe A; Sha M, 2021, Multiplicative and linear dependence in finite fields and on elliptic curves modulo primes, http://dx.doi.org/10.48550/arxiv.2008.00389

Ostafe A, 2021, On a Problem of Lang for Matrix Polynomials, https://arxiv.org/abs/2105.07705v3

Ostafe A; Pottmeyer L; Shparlinski IE, 2021, Perfect powers in value sets and orbits of polynomials, http://dx.doi.org/10.48550/arxiv.1907.12057

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; 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

Mérai L; Ostafe A; Shparlinski IE, 2020, Dynamical irreducibility of polynomials modulo primes, http://dx.doi.org/10.48550/arxiv.1905.11657

Bérczes A; Ostafe A; Shparlinski IE; Silverman JH, 2018, Multiplicative dependence among iterated values of rational functions modulo finitely generated groups, http://dx.doi.org/10.48550/arxiv.1811.04971

Ostafe A; Young M, 2018, On algebraic integers of bounded house and preperiodicity in polynomial semigroup dynamics, https://arxiv.org/abs/1807.11645v2

Gómez-Pérez D; Ostafe A; Sha M, 2018, The Arithmetic of Consecutive Polynomial Sequences over Finite Fields, http://dx.doi.org/10.48550/arxiv.1509.01936

Ostafe A; Sha M; Shparlinski IE; Zannier U, 2018, On multiplicative dependence of values of rational functions and a generalisation of the Northcott theorem, http://dx.doi.org/10.48550/arxiv.1706.05874

Ostafe A; Sha M; Shparlinski IE; Zannier U, 2018, On abelian multiplicatively dependent points on a curve in a torus, http://dx.doi.org/10.48550/arxiv.1704.04694

Chang M-C; D'Andrea C; Ostafe A; Shparlinski IE; Sombra M, 2017, Orbits of Polynomial Dynamical Systems Modulo Primes, http://dx.doi.org/10.48550/arxiv.1702.01976

Ostafe A, 2016, On roots of unity in orbits of rational functions, https://arxiv.org/abs/1603.03983v2

Ostafe A; Sha M, 2015, On the quantitative dynamical Mordell-Lang conjecture, http://dx.doi.org/10.48550/arxiv.1501.02543

Ostafe A, 2015, On some extensions of the Ailon-Rudnick Theorem, https://arxiv.org/abs/1505.03957v3

Ostafe A; Sha M, 2015, Counting dynamical systems over finite fields, http://dx.doi.org/10.48550/arxiv.1505.03618

Ostafe A, 2014, Polynomial Values in Affine Subspaces of Finite Fields, https://arxiv.org/abs/1410.1252v2

Gomez-Perez D; Nicolas AP; Ostafe A; Sadornil D, 2012, Stable Polynomials over Finite Fields, http://dx.doi.org/10.48550/arxiv.1206.4979

Ostafe A; Shparlinski I, 2011, Degree Growth, Linear Independence and Periods of a Class of Rational Dynamical Systems, http://dx.doi.org/10.48550/arxiv.1109.0575

Blackburn SR; Ostafe A; Shparlinski IE, 2011, On the Distribution of the Subset Sum Pseudorandom Number Generator on Elliptic Curves, https://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, http://dx.doi.org/10.48550/arxiv.1102.1053

Ostafe A; Shparlinski IE, 2010, Pseudorandomness and Dynamics of Fermat Quotients, http://dx.doi.org/10.48550/arxiv.1001.1504

Ostafe A; Shparlinski IE, 2010, Pseudorandom Numbers and Hash Functions from Iterations of Multivariate Polynomials, http://dx.doi.org/10.48550/arxiv.0908.4519

Ferguson R; Hoffman C; Luca F; Ostafe A; Shparlinski I, 2010, Some Additive Combinatorics Problems in Matrix Rings, http://dx.doi.org/10.48550/arxiv.0902.3482

Ostafe A; Shparlinski IE, 2009, On the Length of Critical Orbits of Stable Quadratic Polynomials, http://dx.doi.org/10.48550/arxiv.0909.3972

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

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