By Professor Igor Shparlinski

Preprints

Borda B; Munsch M; Shparlinski I, 2023, Pointwise and correlation bounds on Dedekind sums over small subgroups, http://arxiv.org/abs/2305.04304v5

Bulinski K; Ostafe A; Shparlinski IE, 2023, Counting embeddings of free groups into $\mathrm{SL}_2(\mathbb{Z})$ and its subgroups, http://arxiv.org/abs/2304.10980v1

Garaev MZ; Shparlinski IE, 2023, On some congruences and exponential sums, http://arxiv.org/abs/2304.08689v1

Garaev MZ; Shparlinski IE, 2023, On the distribution of modular inverses from short intervals, http://arxiv.org/abs/2304.07953v1

Brandes J; Chen C; Shparlinski IE, 2023, Local mean value estimates for Weyl sums, http://arxiv.org/abs/2303.11913v1

Mérai L; Shparlinski IE, 2023, Distribution of recursive matrix pseudorandom number generator modulo prime powers, http://arxiv.org/abs/2302.03964v1

Shparlinski IE, 2023, On the number of Diophantine $m$-tuples in finite fields, http://arxiv.org/abs/2301.04063v1

Hauck M; Shparlinski IE, 2022, Smooth numbers with few non-zero binary digits, http://arxiv.org/abs/2212.10209v2

Mérai L; Shparlinski IE; Winterhof A, 2022, Character sums over sparse elements of finite fields, http://arxiv.org/abs/2211.08452v1

Ostafe A; Shparlinski IE; Voloch JF, 2022, Weil Sums over Small Subgroups, http://arxiv.org/abs/2211.07739v1

Abdalaoui EHE; Shparlinski IE; Steiner RS, 2022, Chowla and Sarnak Conjectures for Kloosterman Sums, http://dx.doi.org/10.1002/mana.202200480

Fouvry É; Shparlinski IE, 2022, On character sums with determinants, http://arxiv.org/abs/2210.15761v2

Mans B; Sha M; Shparlinski IE; Sutantyo D, 2022, Functional graphs of families of quadratic polynomials, http://arxiv.org/abs/2208.01885v2

Mans B; Sha M; Shparlinski IE; Sutantyo D, 2022, Functional graphs of families of quadratic polynomials, http://dx.doi.org/10.48550/arxiv.2208.01885

Banks W; Shparlinski IE, 2022, On the greatest common divisor of integer parts of polynomials, http://arxiv.org/abs/2205.00253v3

Kerr B; Shparlinski IE; Wu X; Xi P, 2022, Bounds on bilinear forms with Kloosterman sums, http://arxiv.org/abs/2204.05038v5

Habegger P; Ostafe A; Shparlinski IE, 2022, Integer matrices with a given characteristic polynomial and multiplicative dependence of matrices, http://arxiv.org/abs/2203.03880v5

Shparlinski IE, 2022, Multiplicative Properties of Hilbert Cubes, http://arxiv.org/abs/2201.00585v2

Bagshaw C; Shparlinski IE, 2021, Energy bounds, bilinear sums and their applications in function fields, http://arxiv.org/abs/2112.02257v1

Bag N; Shparlinski IE, 2021, Bounds on bilinear sums of Kloosterman sums, http://arxiv.org/abs/2111.07311v1

Shparlinski IE, 2021, On the Glasner property for matrices with polynomial entries, http://arxiv.org/abs/2111.05644v1

Ostafe A; Shparlinski IE; Voloch JF, 2021, Equations and character sums with matrix powers, Kloosterman sums over small subgroups and quantum ergodicity, http://arxiv.org/abs/2110.10941v1

Kaminski M; Shparlinski IE; Waldschmidt M, 2021, On sets of linear forms of maximal complexity, http://dx.doi.org/10.1007/s00037-022-00234-5

Ostafe A; Shparlinski IE, 2021, Additive energy of cyclic matrix groups and character sums with matrix exponential functions, http://dx.doi.org/10.48550/arxiv.2108.13146

Baker RC; Chen C; Shparlinski IE, 2021, Large Weyl sums and Hausdorff dimension, http://dx.doi.org/10.48550/arxiv.2108.10439

Baker RC; Chen C; Shparlinski IE, 2021, Bounds on the Norms of Maximal Operators on Weyl Sums, http://dx.doi.org/10.48550/arxiv.2107.13674

Shparlinski IE; Thuswaldner JM, 2021, Weyl sums over integers with digital restrictions, http://dx.doi.org/10.48550/arxiv.2105.04835

Baker RC; Munsch M; Shparlinski IE, 2021, Additive energy and a large sieve inequality for sparse sequences, http://dx.doi.org/10.48550/arxiv.2103.12659

Kerr B; Shkredov ID; Shparlinski IE; Zaharescu A, 2021, Energy bounds for modular roots and their applications, http://dx.doi.org/10.48550/arxiv.2103.09405

Ghioca D; Shparlinski I, 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

Ghioca D; Ostafe A; Saleh S; Shparlinski IE, 2021, On sparsity of representations of polynomials as linear combinations of exponential functions, http://dx.doi.org/10.48550/arxiv.2102.01949

Ghioca D; Ostafe A; Saleh S; Shparlinski IE, 2020, A sparsity result for the Dynamical Mordell-Lang Conjecture in positive characteristic, http://dx.doi.org/10.48550/arxiv.2012.13711

Brandes J; Shparlinski IE, 2020, Two-dimensional Weyl sums failing square-root cancellation along lines, http://dx.doi.org/10.48550/arxiv.2012.08877

Banks W; Shparlinski I, 2020, On a conjecture of Soundararajan, http://dx.doi.org/10.48550/arxiv.2009.06800

Shkredov ID; Shparlinski IE; Zaharescu A, 2020, On the distribution of modular square roots of primes, http://dx.doi.org/10.48550/arxiv.2009.03460

Mérai L; Shparlinski IE, 2020, On the Dynamical System Generated by the Möbius transformation at Prime Times, http://dx.doi.org/10.48550/arxiv.2009.01089

Kerr B; Mello J; Shparlinski IE, 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

Shparlinski IE; Wang Q, 2020, Exponential sums with sparse polynomials over finite fields, http://dx.doi.org/10.48550/arxiv.2007.14551

Karpinski M; Shparlinski I, 2020, Noisy polynomial interpolation modulo prime powers, http://dx.doi.org/10.48550/arxiv.2006.05685

Ostafe A; Shparlinski I, 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

Konyagin SV; Shparlinski IE; Vyugin IV, 2020, Polynomial Equations in Subgroups and Applications, http://dx.doi.org/10.48550/arxiv.2005.05315

Kerr B; Mello J; Shparlinski I, 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

di Benedetto D; Garaev MZ; García VC; González-Sánchez D; Shparlinski IE; Trujillo CA, 2020, New estimates for exponential sums over multiplicative subgroups and intervals in prime fields, http://dx.doi.org/10.48550/arxiv.2003.06165

Macourt S; Petridis G; Shkredov ID; Shparlinski IE, 2020, Bounds of Trilinear and Trinomial Exponential Sums, http://dx.doi.org/10.48550/arxiv.2003.03493

Chen C; Shparlinski IE, 2020, Hybrid bounds on two-parametric family Weyl sums along smooth curves, http://dx.doi.org/10.48550/arxiv.2003.02419

Li R; Shparlinski IE, 2020, Effective bounds on multiplicatively dependent orbits of integer polynomials modulo S-integers, http://dx.doi.org/10.48550/arxiv.2001.09721

Kerr B; Mérai L; Shparlinski IE, 2020, On digits of Mersenne numbers, http://dx.doi.org/10.48550/arxiv.2001.03380

Chen C; Shparlinski IE, 2019, Restricted mean value theorems and metric theory of restricted Weyl sums, http://dx.doi.org/10.48550/arxiv.1912.01307

Dąbrowski A; Pomykała J; Shparlinski IE, 2019, On oracle factoring of integers, http://dx.doi.org/10.48550/arxiv.1912.00345

Chen C; Shparlinski IE, 2019, On a Hybrid Version of the Vinogradov Mean Value Theorem, http://dx.doi.org/10.48550/arxiv.1910.07329

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