Select Publications
Preprints
2022, On character sums with determinants, http://arxiv.org/abs/2210.15761v2
,2022, Functional graphs of families of quadratic polynomials, http://arxiv.org/abs/2208.01885v2
,2022, Functional graphs of families of quadratic polynomials, http://dx.doi.org/10.48550/arxiv.2208.01885
,2022, On the greatest common divisor of integer parts of polynomials, http://arxiv.org/abs/2205.00253v3
,2022, Bounds on bilinear forms with Kloosterman sums, http://arxiv.org/abs/2204.05038v5
,2022, Integer matrices with a given characteristic polynomial and multiplicative dependence of matrices, http://arxiv.org/abs/2203.03880v5
,2022, Multiplicative Properties of Hilbert Cubes, http://arxiv.org/abs/2201.00585v2
,2021, Energy bounds, bilinear sums and their applications in function fields, http://arxiv.org/abs/2112.02257v1
,2021, Bounds on bilinear sums of Kloosterman sums, http://arxiv.org/abs/2111.07311v1
,2021, On the Glasner property for matrices with polynomial entries, http://arxiv.org/abs/2111.05644v1
,2021, Equations and character sums with matrix powers, Kloosterman sums over small subgroups and quantum ergodicity, http://arxiv.org/abs/2110.10941v1
,2021, On sets of linear forms of maximal complexity, http://dx.doi.org/10.1007/s00037-022-00234-5
,2021, Additive energy of cyclic matrix groups and character sums with matrix exponential functions, http://dx.doi.org/10.48550/arxiv.2108.13146
,2021, Large Weyl sums and Hausdorff dimension, http://dx.doi.org/10.48550/arxiv.2108.10439
,2021, Bounds on the Norms of Maximal Operators on Weyl Sums, http://dx.doi.org/10.48550/arxiv.2107.13674
,2021, Weyl sums over integers with digital restrictions, http://dx.doi.org/10.48550/arxiv.2105.04835
,2021, Additive energy and a large sieve inequality for sparse sequences, http://dx.doi.org/10.48550/arxiv.2103.12659
,2021, Energy bounds for modular roots and their applications, http://dx.doi.org/10.48550/arxiv.2103.09405
,2021, Order of torsion for reduction of linearly independent points for a family of Drinfeld modules, http://dx.doi.org/10.48550/arxiv.2103.00641
,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, Two-dimensional Weyl sums failing square-root cancellation along lines, http://dx.doi.org/10.48550/arxiv.2012.08877
,2020, On a conjecture of Soundararajan, http://dx.doi.org/10.48550/arxiv.2009.06800
,2020, On the distribution of modular square roots of primes, http://dx.doi.org/10.48550/arxiv.2009.03460
,2020, On the Dynamical System Generated by the Möbius transformation at Prime Times, http://dx.doi.org/10.48550/arxiv.2009.01089
,2020, On elements of large order of elliptic curves and multiplicative dependent images of rational functions over finite fields, http://dx.doi.org/10.48550/arxiv.2008.00433
,2020, Exponential sums with sparse polynomials over finite fields, http://dx.doi.org/10.48550/arxiv.2007.14551
,2020, Noisy polynomial interpolation modulo prime powers, http://dx.doi.org/10.48550/arxiv.2006.05685
,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
,2020, Polynomial Equations in Subgroups and Applications, http://dx.doi.org/10.48550/arxiv.2005.05315
,2020, An effective local-global principle for algebraic varieties and the sum product problem in finite fields, http://dx.doi.org/10.48550/arxiv.2005.02923
,2020, New estimates for exponential sums over multiplicative subgroups and intervals in prime fields, http://dx.doi.org/10.48550/arxiv.2003.06165
,2020, Bounds of Trilinear and Trinomial Exponential Sums, http://dx.doi.org/10.48550/arxiv.2003.03493
,2020, Hybrid bounds on two-parametric family Weyl sums along smooth curves, http://dx.doi.org/10.48550/arxiv.2003.02419
,2020, Effective bounds on multiplicatively dependent orbits of integer polynomials modulo S-integers, http://dx.doi.org/10.48550/arxiv.2001.09721
,2020, On digits of Mersenne numbers, http://dx.doi.org/10.48550/arxiv.2001.03380
,2019, Restricted mean value theorems and metric theory of restricted Weyl sums, http://dx.doi.org/10.48550/arxiv.1912.01307
,2019, On oracle factoring of integers, http://dx.doi.org/10.48550/arxiv.1912.00345
,2019, On a Hybrid Version of the Vinogradov Mean Value Theorem, http://dx.doi.org/10.48550/arxiv.1910.07329
,2019, Lower bounds for periods of Ducci sequences, http://dx.doi.org/10.48550/arxiv.1909.04462
,2019, Möbius Randomness Law for Frobenius Traces, http://dx.doi.org/10.48550/arxiv.1909.00969
,2019, Discriminants of Fields Generated by Polynomials of Given Height, http://dx.doi.org/10.48550/arxiv.1909.00135
,2019, Bilinear forms in Weyl sums for modular square roots and applications, http://dx.doi.org/10.48550/arxiv.1908.10143
,2019, Perfect powers in value sets and orbits of polynomials, http://dx.doi.org/10.48550/arxiv.1907.12057
,2019, Congruences with intervals and arbitrary sets, http://dx.doi.org/10.48550/arxiv.1907.03943
,2019, Small values of Weyl sums, http://dx.doi.org/10.48550/arxiv.1907.03101
,2019, Dynamical irreducibility of polynomials modulo primes, http://dx.doi.org/10.48550/arxiv.1905.11657
,2019, Unlikely intersections over finite fields: polynomial orbits in small subgroups, http://dx.doi.org/10.48550/arxiv.1904.12621
,2019, Hausdorff dimension of the large values of Weyl sums, http://dx.doi.org/10.48550/arxiv.1904.04457
,2019, Double Sums of Kloosterman Sums in Finite Fields, http://dx.doi.org/10.48550/arxiv.1903.10070
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