Select Publications

Journal articles

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

Ostafe A; Shparlinski IE, 2021, 'Additive energy of cyclic matrix groups and character sums with matrix exponential functions', , http://arxiv.org/abs/2108.13146v2

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

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

Ostafe A, 2021, 'On a Problem of Lang for Matrix Polynomials', , http://arxiv.org/abs/2105.07705v2

Ghioca D; Ostafe A; Saleh S; Shparlinski IE, 2021, 'On sparsity of representations of polynomials as linear combinations of exponential functions', , http://arxiv.org/abs/2102.01949v1

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

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

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

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

Dietmann R; Ostafe A; Shparlinski IE, 2019, 'Discriminants of Fields Generated by Polynomials of Given Height', , http://arxiv.org/abs/1909.00135v2

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

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, vol. 5, https://arxiv.org/abs/1706.05874

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

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

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

Ostafe A; Sha M, 2018, 'Counting Dynamical Systems over Finite Fields', Contemporary Mathematics, pp. 187 - 203, http://dx.doi.org/10.1090/conm/669

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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), vol. 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), vol. 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, vol. 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, vol. 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, vol. 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, vol. 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, vol. 79, pp. 501 - 511, http://dx.doi.org/10.1090/S0025-5718-09-02271-6


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