By Associate Professor Alina Ostafe

Journal articles

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', , http://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', 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, 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

Preprints

Ostafe A; Shparlinski IE, 2024, On the frequency of primes preserving dynamical irreducibility of polynomials, http://arxiv.org/abs/2407.20464v1

Afifurrahman M; Kuperberg V; Ostafe A; Shparlinski IE, 2024, Statistics of ranks, determinants and characteristic polynomials of rational matrices, http://arxiv.org/abs/2401.10086v2

Ostafe A; Shparlinski IE, 2023, On the sparsity of non-diagonalisable integer matrices and matrices with a given discriminant, http://arxiv.org/abs/2312.12626v2

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://arxiv.org/abs/2310.09704v1

Mohammadi A; Ostafe A; Shparlinski I, 2023, On some matrix counting problems, http://arxiv.org/abs/2310.05038v2

Bulinski K; Ostafe A; Shparlinski IE, 2023, Counting embeddings of free groups into $\mathrm{SL}_2(\mathbb{Z})$ and its subgroups, http://arxiv.org/abs/2304.10980v1

Ostafe A; Shparlinski IE; Voloch JF, 2022, Weil Sums over Small Subgroups, http://arxiv.org/abs/2211.07739v1

Ferraguti A; Ostafe A; Zannier U, 2022, Cyclotomic and abelian points in backward orbits of rational functions, http://arxiv.org/abs/2203.10034v2

Habegger P; Ostafe A; Shparlinski IE, 2022, Integer matrices with a given characteristic polynomial and multiplicative dependence of matrices, http://arxiv.org/abs/2203.03880v5

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

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

Bérczes A; Bugeaud Y; Győry K; Mello J; Ostafe A; Sha M, 2021, Multiplicative dependence of rational values modulo approximate finitely generated groups, http://dx.doi.org/10.48550/arxiv.2107.05371

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

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

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

Dietmann R; Ostafe A; Shparlinski IE, 2019, Discriminants of Fields Generated by Polynomials of Given Height, http://dx.doi.org/10.48550/arxiv.1909.00135

Ostafe A; Pottmeyer L; Shparlinski IE, 2019, Perfect powers in value sets and orbits of polynomials, http://dx.doi.org/10.48550/arxiv.1907.12057

Mérai L; Ostafe A; Shparlinski IE, 2019, 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; 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

Ostafe A; Sha M; Shparlinski IE; Zannier U, 2017, 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

Gómez-Pérez D; Ostafe A; Sha M, 2015, The Arithmetic of Consecutive Polynomial Sequences over Finite Fields, http://dx.doi.org/10.48550/arxiv.1509.01936

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

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

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

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, http://dx.doi.org/10.48550/arxiv.1102.1053

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