By Professor Igor Shparlinski

Preprints

Ostafe A; Shparlinski IE, 2025, Counting integer matrices with square-free determinants, http://arxiv.org/abs/2503.13768v1

Koh D; Shparlinski IE, 2025, Mean value theorems for rational exponential sums, http://arxiv.org/abs/2503.10933v1

Ostafe A; Pomerance C; Shparlinski IE, 2025, Counting solvable $\mathcal S$-unit equations and linear recurrence sequences with zeros, http://arxiv.org/abs/2503.03985v1

Manning A; Ostafe A; Shparlinski IE, 2025, Counting matrices over finite rank multiplicative groups, http://arxiv.org/abs/2502.07100v1

Bérczes A; Hajdu L; Ostafe A; Shparlinski IE, 2025, Multiplicative dependence in linear recurrence sequences, http://arxiv.org/abs/2501.17365v1

Klurman O; Shparlinski IE; Teräväinen J, 2024, On Artin's conjecture on average and short character sums, http://arxiv.org/abs/2412.13355v1

Bhakta S; Shparlinski I, 2024, Exponential Sums with Sparse Polynomials and Distribution of the Power Generator, http://arxiv.org/abs/2412.07989v2

Blomer V; Risager MS; Shparlinski IE, 2024, Triple sums of Kloosterman sums and the discrepancy of modular inverses, http://arxiv.org/abs/2411.17823v2

Shao X; Shparlinski IE; Wijaya LP, 2024, Sums of Kloosterman sums over square-free and smooth integers, http://arxiv.org/abs/2411.12113v1

Kurlberg P; Ostafe A; Rudnick Z; Shparlinski IE, 2024, On quantum ergodicity for higher dimensional cat maps, http://arxiv.org/abs/2411.05997v1

Shparlinski IE; Voloch JF, 2024, On the Waring problem with Dickson polynomials modulo a prime, http://arxiv.org/abs/2410.08732v1

Garaev MZ; Pardo JC; Shparlinski IE, 2024, Binary and ternary congruences involving intervals and sets modulo a prime, http://dx.doi.org/10.1017/S0004972725000152

Shkredov ID; Shparlinski IE, 2024, On the determinants of matrices with elements from arbitrary sets, http://arxiv.org/abs/2408.04350v1

Ostafe A; Shparlinski IE, 2024, On the frequency of primes preserving dynamical irreducibility of polynomials, http://arxiv.org/abs/2407.20464v1

Shparlinski IE, 2024, Exponential sums over integers without large prime divisors, http://arxiv.org/abs/2404.10278v1

Fouvry É; Shparlinski IE; Xi P, 2024, Estimates for trilinear and quadrilinear character sums, http://arxiv.org/abs/2404.09295v4

Perucca A; Shparlinski IE, 2024, Uniform bounds for the density in Artin's conjecture on primitive roots, http://arxiv.org/abs/2401.11589v1

Afifurrahman M; Kuperberg V; Ostafe A; Shparlinski IE, 2024, Statistics of ranks, determinants and characteristic polynomials of rational matrices, http://arxiv.org/abs/2401.10086v2

Iyer S; Shparlinski I, 2024, Character sums over elements of extensions of finite fields with restricted coordinates

Ostafe A; Shparlinski IE, 2023, On the sparsity of non-diagonalisable integer matrices and matrices with a given discriminant, http://arxiv.org/abs/2312.12626v2

Shparlinski IE, 2023, Rational numbers with small denominators in short intervals, http://arxiv.org/abs/2311.16640v2

Baird R; Kerr B; Shparlinski I, 2023, Bohr sets generated by polynomials and Coppersmith's method in many variables, http://arxiv.org/abs/2310.20342v1

Mérai L; Shparlinski IE, 2023, Number of characteristic polynomials of matrices with bounded height, http://arxiv.org/abs/2310.09052v2

Mohammadi A; Ostafe A; Shparlinski I, 2023, On some matrix counting problems, http://arxiv.org/abs/2310.05038v2

Garaev M; Rudnick Z; Shparlinski I, 2023, On a family of sparse exponential sums, http://arxiv.org/abs/2309.11887v1

Munsch M; Shparlinski IE, 2023, Moments and non-vanishing of $L$-functions over thin subgroups, http://arxiv.org/abs/2309.10207v3

Bulinski K; Shparlinski IE, 2023, Counting elements of the congruence subgroup, http://dx.doi.org/10.4153/S0008439524000365

Dubickas A; Sha M; Shparlinski IE, 2023, Euclidean minima of algebraic number fields, http://arxiv.org/abs/2307.10880v1

Shparlinski IE; Wijaya LP, 2023, On Nonzero Coefficients of Binary Cyclotomic Polynomials, http://arxiv.org/abs/2307.07229v2

Kerr B; Mohammadi A; Shparlinski IE, 2023, Additive energy of polynomial images, http://arxiv.org/abs/2306.10677v1

Browning T; Shparlinski I, 2023, Square-free values of random polynomials, http://arxiv.org/abs/2305.15493v1

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

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