Select Publications
Books
2014, Algebraic Curves and Finite Fields Introduction, Niederreiter H; Ostafe A; Panario D; Winterhof A, (eds.), WALTER DE GRUYTER GMBH
,Book Chapters
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
,2016, 'Counting dynamical systems over finite fields', in Contemporary Mathematics, pp. 187 - 203, http://dx.doi.org/10.1090/conm/669/13429
,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
,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
2024, 'Discriminants of fields generated by polynomials of given height', Israel Journal of Mathematics, 260, pp. 73 - 103, http://dx.doi.org/10.1007/s11856-023-2557-x
,2024, 'Counting embeddings of free groups into $\mathrm{SL}_2(\mathbb{Z})$ and its subgroups', ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE, pp. 12 - 12, http://dx.doi.org/10.2422/2036-2145.202307_011
,2024, 'Cyclotomic and abelian points in backward orbits of rational functions', Advances in Mathematics, 438, http://dx.doi.org/10.1016/j.aim.2023.109463
,2024, 'Weil Sums over Small Subgroups', Mathematical Proceedings of the Cambridge Philosophical Society, 176, pp. 39 - 53, http://dx.doi.org/10.1017/S0305004123000415
,2024, 'Explicit bounds for the solutions of superelliptic equations over number fields', Forum Mathematicum, http://dx.doi.org/10.1515/forum-2023-0381
,2024, 'Statistics of ranks, determinants and characteristic polynomials of rational matrices', Forum Mathematicum, http://dx.doi.org/10.1515/forum-2024-0114
,2023, 'Corrigendum to: On a problem of Lang for matrix polynomials (Bulletin of the London Mathematical Society, (2022), 54, 5, (1552-1567), 10.1112/blms.12642)', Bulletin of the London Mathematical Society, 55, pp. 2086, http://dx.doi.org/10.1112/blms.12874
,2023, 'Equations and Character Sums with Matrix Powers, Kloosterman Sums over Small Subgroups, and Quantum Ergodicity', International Mathematics Research Notices, 2023, pp. 14196 - 14238, http://dx.doi.org/10.1093/imrn/rnac226
,2022, 'On a problem of Lang for matrix polynomials', Bulletin of the London Mathematical Society, 54, pp. 1552 - 1567, http://dx.doi.org/10.1112/blms.12642
,2022, 'Perfect powers in value sets and orbits of polynomials', The New York Journal of Mathematics
,2022, 'On the Skolem problem and some related questions for parametric families of linear recurrence sequences', Canadian Journal of Mathematics, 74, pp. 773 - 792, http://dx.doi.org/10.4153/S0008414X21000080
,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
,2021, 'A SPARSITY RESULT for the DYNAMICAL MORDELL-LANG CONJECTURE in POSITIVE CHARACTERISTIC', Bulletin of the Australian Mathematical Society, 104, pp. 381 - 390, http://dx.doi.org/10.1017/S0004972721000083
,2021, 'Additive energy of cyclic matrix groups and character sums with matrix exponential functions', , http://arxiv.org/abs/2108.13146v2
,2021, 'Dynamical irreducibility of polynomials modulo primes', Mathematische Zeitschrift, 298, pp. 1187 - 1199, http://dx.doi.org/10.1007/s00209-020-02630-5
,2021, 'Multiplicative and Linear Dependence in Finite Fields and on Elliptic Curves Modulo Primes', International Mathematics Research Notices, 2022, pp. 16094 - 16137, http://dx.doi.org/10.1093/imrn/rnab171
,2021, 'Multiplicative dependence of rational values modulo approximate finitely generated groups', , http://arxiv.org/abs/2107.05371v3
,2021, 'On a Problem of Lang for Matrix Polynomials', , http://arxiv.org/abs/2105.07705v3
,2021, 'Perfect powers in value sets and orbits of polynomials', NEW YORK JOURNAL OF MATHEMATICS, 27, pp. 903 - 917, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000669490500001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1
,2020, 'Multiplicative and linear dependence in finite fields and on elliptic curves modulo primes', , http://arxiv.org/abs/2008.00389v2
,2019, 'On algebraic integers of bounded house and preperiodicity in polynomial semigroup dynamics', Transactions of the American Mathematical Society, 00, http://dx.doi.org/10.1090/tran/7974
,2019, 'Discriminants of Fields Generated by Polynomials of Given Height', , http://arxiv.org/abs/1909.00135v2
,2019, 'Polynomial values in affine subspaces of finite fields', Journal d'Analyse Mathematique, 138, pp. 49 - 81, http://dx.doi.org/10.1007/s11854-019-0021-y
,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
,2018, 'On multiplicative dependence of values of rational functions and a generalisation of the Northcott theorem', MICHIGAN MATHEMATICAL JOURNAL, 5, https://arxiv.org/abs/1706.05874
,2018, 'Reductions modulo primes of systems of polynomial equations and algebraic dynamical systems', Transactions of the American Mathematical Society, 371, pp. 1169 - 1198, http://dx.doi.org/10.1090/tran/7437
,2018, 'The Arithmetic of Consecutive Polynomial Sequences over Finite Fields', Finite Fields and Their Applications, 50, pp. 35 - 65, http://dx.doi.org/10.1016/j.ffa.2017.11.002
,2018, 'Counting dynamical systems over finite fields', Contemporary Mathematics, 669, http://dx.doi.org/10.1090/conm/669
,2018, 'Counting Dynamical Systems over Finite Fields', Contemporary Mathematics, pp. 187 - 203, http://dx.doi.org/10.1090/conm/669
,2018, 'On abelian multiplicatively dependent points on a curve in a torus', The Quarterly Journal of Mathematics, http://dx.doi.org/10.1093/qmath/hax045
,2018, 'On Some Extensions of the Ailon–Rudnick Theorem', Monatshefte für Mathematik, 181, pp. 451 - 471, http://dx.doi.org/10.1007/s00605-016-0911-3
,2018, 'Orbits of Polynomial Dynamical Systems Modulo Primes', Proceedings of the American Mathematical Society, 146, pp. 2015 - 2025, http://dx.doi.org/10.1090/proc/13904
,2018, 'Stable polynomials over finite fields', Revista Matematica Iberoamericana, 30, pp. 523 - 535, http://dx.doi.org/10.4171/rmi/791
,2016, 'On roots of unity in orbits of rational functions', Proceedings of the American Mathematical Society, http://dx.doi.org/10.1090/proc/13433
,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, 164, pp. 433 - 437, http://dx.doi.org/10.1016/j.jnt.2016.01.014
,2016, 'Common composites of triangular polynomial systems and hash functions', JOURNAL OF SYMBOLIC COMPUTATION, 72, pp. 182 - 195, http://dx.doi.org/10.1016/j.jsc.2015.02.005
,2015, 'On the quantitative dynamical Mordell-Lang conjecture', Journal of Number Theory, 156, pp. 161 - 182, http://dx.doi.org/10.1016/j.jnt.2015.04.011
,2014, 'Algebraic entropy, automorphisms and sparsity of algebraic dynamical systems and pseudorandom number generators', Mathematics of Computation, 83, pp. 1535 - 1550, http://dx.doi.org/10.1090/S0025-5718-2013-02780-9
,2014, 'On irreducible divisors of iterated polynomials', Revista Matematica Iberoamericana, 30, pp. 1123 - 1134, http://dx.doi.org/10.4171/rmi/809
,2014, 'On the Carlitz rank of permutations ofFqand pseudorandom sequences', Journal of Complexity, 30, pp. 279 - 289, http://dx.doi.org/10.1016/j.jco.2013.11.001
,2012, 'On the concentration of points of polynomial maps and applications', Mathematische Zeitschrift, 272, pp. 825 - 837, http://dx.doi.org/10.1007/s00209-011-0959-7
,2012, 'Multiplicative character sums and products of sparse integers in residue classes', Periodica Mathematica Hungarica, 64, pp. 247 - 255, http://dx.doi.org/10.1007/s10998-012-6771-2
,2012, 'On stable quadratic polynomials', Glasgow Mathematical Journal, 54, pp. 359 - 369, http://dx.doi.org/10.1017/S001708951200002X
,2012, 'Pseudorandom vector sequences of maximal period generated by triangular polynomial dynamical systems', Designs, Codes, and Cryptography, 63, pp. 59 - 72, http://dx.doi.org/10.1007/s10623-011-9535-8
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