By Associate Professor Alina Ostafe

Journal articles

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 I, 2012, 'Degree growth, linear independence and periods of a class of rational dynamical systems', Contemporary Mathematics, 574, pp. 131 - 143, http://dx.doi.org/10.1090/conm/574/11426

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

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

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

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

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

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

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

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

Conference Papers

Ostafe A; Thomson D; Winterhof A, 2012, 'On the Waring Problem with multivariate Dickson polynomials', in Contemporary Mathematics, American Mathematical Society (AMS), pp. 153 - 161, http://dx.doi.org/10.1090/conm/579/11527

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

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