Select Publications

Books

Niederreiter H; Ostafe A; Panario D; Winterhof A, 2014, Algebraic Curves and Finite Fields Introduction, Niederreiter H; Ostafe A; Panario D; Winterhof A, (eds.), Radon Series on Computational and Applied Mathematics, WALTER DE GRUYTER GMBH, http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000352560600001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Book Chapters

Ostafe A; Shparlinski IE, 2017, 'Orbits of algebraic dynamical systems in subgroups and subfields', in Elsholtz C; Grabner P (ed.), Number Theory - Diophantine Problems, Uniform Distribution and Applications: Festschrift in Honour of Robert F. Tichy's 60th Birthday, Springer, pp. 347 - 368, http://dx.doi.org/10.1007/978-3-319-55357-3_18

Ostafe A; Sha M, 2016, 'Counting dynamical systems over finite fields', in Contemporary Mathematics, pp. 187 - 203, http://dx.doi.org/10.1090/conm/669/13429

Ostafe A, 2013, 'Iterations of Rational Functions: Some Algebraic and Arithmetic Aspects', in Finite Fields and Their Applications, DE GRUYTER, pp. 197 - 232, http://dx.doi.org/10.1515/9783110283600.197

Ostafe A; Winterhof A, 2013, 'Some applications of character sums.', in Mullen GL; Panario D (ed.), Handbook of Finite Fields, CRC Press, pp. 170 - 184, https://www.crcpress.com/product/isbn/9781439873786

Edited Books

Niederreiter H; Ostafe A; Panario D; Winterhof A, (eds.), 2014, Algebraic Curves and Finite Fields, WALTER DE GRUYTER GMBH, https://www.degruyter.com/view/product/207742

Journal articles

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

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, http://dx.doi.org/10.1112/jlms.12554

Ostafe A, 2022, 'On a problem of Lang for matrix polynomials', Bulletin of the London Mathematical Society, http://dx.doi.org/10.1112/blms.12642

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

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, http://dx.doi.org/10.1093/imrn/rnab171

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

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


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