Select Publications
Preprints
2024, Statistics of ranks, determinants and characteristic polynomials of rational matrices, , http://arxiv.org/abs/2401.10086v2
,2023, On the sparsity of integer matrices with a given discriminant, , http://arxiv.org/abs/2312.12626v1
,2023, Explicit bounds for the solutions of superelliptic equations over number fields, , http://arxiv.org/abs/2310.09704v1
,2023, On some matrix counting problems, , http://arxiv.org/abs/2310.05038v2
,2023, Counting embeddings of free groups into $\mathrm{SL}_2(\mathbb{Z})$ and its subgroups, , http://arxiv.org/abs/2304.10980v1
,2022, Weil Sums over Small Subgroups, , http://arxiv.org/abs/2211.07739v1
,2022, Cyclotomic and abelian points in backward orbits of rational functions, , http://arxiv.org/abs/2203.10034v2
,2022, Integer matrices with a given characteristic polynomial and multiplicative dependence of matrices, , http://arxiv.org/abs/2203.03880v4
,2021, Equations and character sums with matrix powers, Kloosterman sums over small subgroups and quantum ergodicity, , http://arxiv.org/abs/2110.10941v1
,2021, Additive energy of cyclic matrix groups and character sums with matrix exponential functions, , http://dx.doi.org/10.48550/arxiv.2108.13146
,2021, Multiplicative dependence of rational values modulo approximate finitely generated groups, , http://dx.doi.org/10.48550/arxiv.2107.05371
,2021, On sparsity of representations of polynomials as linear combinations of exponential functions, , http://dx.doi.org/10.48550/arxiv.2102.01949
,2020, A sparsity result for the Dynamical Mordell-Lang Conjecture in positive characteristic, , http://dx.doi.org/10.48550/arxiv.2012.13711
,2020, Multiplicative and linear dependence in finite fields and on elliptic curves modulo primes, , http://dx.doi.org/10.48550/arxiv.2008.00389
,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
,2019, Discriminants of Fields Generated by Polynomials of Given Height, , http://dx.doi.org/10.48550/arxiv.1909.00135
,2019, Perfect powers in value sets and orbits of polynomials, , http://dx.doi.org/10.48550/arxiv.1907.12057
,2019, Dynamical irreducibility of polynomials modulo primes, , http://dx.doi.org/10.48550/arxiv.1905.11657
,2018, Multiplicative dependence among iterated values of rational functions modulo finitely generated groups, , http://dx.doi.org/10.48550/arxiv.1811.04971
,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
,2017, On abelian multiplicatively dependent points on a curve in a torus, , http://dx.doi.org/10.48550/arxiv.1704.04694
,2017, Orbits of Polynomial Dynamical Systems Modulo Primes, , http://dx.doi.org/10.48550/arxiv.1702.01976
,2015, The Arithmetic of Consecutive Polynomial Sequences over Finite Fields, , http://dx.doi.org/10.48550/arxiv.1509.01936
,2015, Reductions Modulo Primes of Systems of Polynomial Equations and Algebraic Dynamical Systems, , http://dx.doi.org/10.48550/arxiv.1505.05814
,2015, Counting dynamical systems over finite fields, , http://dx.doi.org/10.48550/arxiv.1505.03618
,2015, On the quantitative dynamical Mordell-Lang conjecture, , http://dx.doi.org/10.48550/arxiv.1501.02543
,2012, Stable Polynomials over Finite Fields, , http://dx.doi.org/10.48550/arxiv.1206.4979
,2011, Degree Growth, Linear Independence and Periods of a Class of Rational Dynamical Systems, , http://dx.doi.org/10.48550/arxiv.1109.0575
,2011, On the Distribution of the Subset Sum Pseudorandom Number Generator on Elliptic Curves, , http://dx.doi.org/10.48550/arxiv.1102.1053
,2010, Pseudorandomness and Dynamics of Fermat Quotients, , http://dx.doi.org/10.48550/arxiv.1001.1504
,2009, On the Length of Critical Orbits of Stable Quadratic Polynomials, , http://dx.doi.org/10.48550/arxiv.0909.3972
,2009, Pseudorandom Numbers and Hash Functions from Iterations of Multivariate Polynomials, , http://dx.doi.org/10.48550/arxiv.0908.4519
,2009, On the Degree Growth in Some Polynomial Dynamical Systems and Nonlinear Pseudorandom Number Generators, , http://dx.doi.org/10.48550/arxiv.0902.3884
,2009, Some Additive Combinatorics Problems in Matrix Rings, , http://dx.doi.org/10.48550/arxiv.0902.3482
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