By Professor Igor Shparlinski

Preprints

Shparlinski I; Sleiman N, 2026, Counting consecutive multiplicatively dependent triples, https://arxiv.org/abs/2609.29408v1

Klurman O; Shparlinski IE; Teräväinen J, 2026, On the generation of multiplicative groups by small primes, https://arxiv.org/abs/2609.25393v1

Shparlinski IE; Xiao Y, 2026, Arithmetic structure of $L_2$-norms of ${\mathrm{SL}}_2(\mathbb{Z})$ matrices, https://arxiv.org/abs/2609.21460v1

Munsch M; Shparlinski I; Sun Y-C; Xiao Y, 2026, Large sieve inequality for sums of Legendre symbols over short intervals, http://dx.doi.org/10.48550/arxiv.2604.23661

Ostafe A; Shparlinski IE, 2026, Counting Irreducible polynomials with coefficients from thin subgroups, http://dx.doi.org/10.48550/arxiv.2601.12968

Ostafe A; Shparlinski IE, 2026, Counting integer matrices with square-free determinants, http://dx.doi.org/10.48550/arxiv.2503.13768

Darbar P; Kerr B; Munsch M; Shparlinski I, 2026, Large values of $L(σ,χ)$ for subgroups of characters, http://dx.doi.org/10.48550/arxiv.2604.02960

Ostafe A; Shparlinski IE, 2026, On the sparsity of non-diagonalisable integer matrices and matrices with a given discriminant, http://dx.doi.org/10.48550/arxiv.2312.12626

Afifurrahman M; Kuperberg V; Ostafe A; Shparlinski IE, 2026, Statistics of ranks, determinants and characteristic polynomials of rational matrices, http://dx.doi.org/10.48550/arxiv.2401.10086

Klurman O; Shparlinski IE; Teräväinen J, 2026, On Artin's conjecture on average and short character sums, http://dx.doi.org/10.48550/arxiv.2412.13355

Shparlinski IE; Xiao Y, 2026, Shifted bilinear sums of Salié sums and the distribution of modular square roots of shifted primes, http://dx.doi.org/10.48550/arxiv.2601.10113

Bérczes A; Bhakta S; Hajdu L; Ostafe A; Shparlinski IE, 2025, Multiplicative dependence in the denominators of points of elliptic curves, http://dx.doi.org/10.48550/arxiv.2510.05462

Bhakta S; Shparlinski IE, 2025, On quantum ergodicity for higher dimensional cat maps modulo prime powers, http://dx.doi.org/10.48550/arxiv.2507.00325

Blomer V; Risager MS; Shparlinski IE, 2025, Triple sums of Kloosterman sums and the discrepancy of modular inverses, http://dx.doi.org/10.48550/arxiv.2411.17823

Mérai L; Shparlinski IE, 2025, On the Dynamical System Generated by the Möbius Transformation at Smooth Times, http://dx.doi.org/10.48550/arxiv.2507.12160

Bhakta S; Shparlinski IE, 2025, On the correlations between character sums of division polynomials under shifts, http://dx.doi.org/10.48550/arxiv.2507.09271

Majeed F; Shparlinski IE, 2025, Mean value theorems with smooth numbers, http://dx.doi.org/10.48550/arxiv.2506.22192

Kurlberg P; Ostafe A; Rudnick Z; Shparlinski IE, 2025, On quantum ergodicity for higher dimensional cat maps, http://dx.doi.org/10.48550/arxiv.2411.05997

Banks WD; Shparlinski IE, 2025, Multiple sums with the Möbius function, http://dx.doi.org/10.48550/arxiv.2506.08787

Drappeau S; Shparlinski IE, 2025, Exponential sums over integers without large prime divisors, http://dx.doi.org/10.48550/arxiv.2404.10278

Fouvry É; Shparlinski IE; Xi P, 2025, Estimates for trilinear and quadrilinear character sums, http://dx.doi.org/10.48550/arxiv.2404.09295

Koh D; Shparlinski IE, 2025, Mean value theorems for rational exponential sums, http://dx.doi.org/10.48550/arxiv.2503.10933

Ostafe A; Pomerance C; Shparlinski IE, 2025, Counting solvable $\mathcal S$-unit equations and linear recurrence sequences with zeros, http://dx.doi.org/10.48550/arxiv.2503.03985

Munsch M; Shparlinski IE, 2025, Moments and non-vanishing of $L$-functions over thin subgroups, http://dx.doi.org/10.48550/arxiv.2309.10207

Mérai L; Shparlinski IE, 2025, Number of characteristic polynomials of matrices with bounded height, http://dx.doi.org/10.48550/arxiv.2310.09052

Manning A; Ostafe A; Shparlinski IE, 2025, Counting matrices over finite rank multiplicative groups, http://dx.doi.org/10.48550/arxiv.2502.07100

Bérczes A; Hajdu L; Ostafe A; Shparlinski IE, 2025, Multiplicative dependence in linear recurrence sequences, http://dx.doi.org/10.48550/arxiv.2501.17365

Shparlinski IE; Wijaya LP, 2024, On Nonzero Coefficients of Binary Cyclotomic Polynomials, http://dx.doi.org/10.48550/arxiv.2307.07229

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

Shao X; Shparlinski IE; Wijaya LP, 2024, Sums of Kloosterman sums over square-free and smooth integers, http://dx.doi.org/10.48550/arxiv.2411.12113

Shparlinski IE; Voloch JF, 2024, On the Waring problem with Dickson polynomials modulo a prime, http://dx.doi.org/10.48550/arxiv.2410.08732

Garaev MZ; Pardo JC; Shparlinski IE, 2024, Binary and ternary congruences involving intervals and sets modulo a prime, http://dx.doi.org/10.48550/arxiv.2410.03991

Habegger P; Ostafe A; Shparlinski IE, 2024, Integer matrices with a given characteristic polynomial and multiplicative dependence of matrices, http://dx.doi.org/10.48550/arxiv.2203.03880

Shkredov ID; Shparlinski IE, 2024, On the determinants of matrices with elements from arbitrary sets, http://dx.doi.org/10.48550/arxiv.2408.04350

Ostafe A; Shparlinski IE, 2024, On the frequency of primes preserving dynamical irreducibility of polynomials, http://dx.doi.org/10.48550/arxiv.2407.20464

Shparlinski IE, 2024, Rational numbers with small denominators in short intervals, http://dx.doi.org/10.48550/arxiv.2311.16640

Borda B; Munsch M; Shparlinski I, 2024, Pointwise and correlation bounds on Dedekind sums over small subgroups, http://dx.doi.org/10.48550/arxiv.2305.04304

Perucca A; Shparlinski IE, 2024, Uniform bounds for the density in Artin's conjecture on primitive roots, http://dx.doi.org/10.48550/arxiv.2401.11589

Iyer S; Shparlinski I, 2024, Character sums over elements of extensions of finite fields with restricted coordinates, http://arxiv.org/abs/2309.02948v2

Banks W; Shparlinski IE, 2023, On the greatest common divisor of integer parts of polynomials, http://dx.doi.org/10.48550/arxiv.2205.00253

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

Mohammadi A; Ostafe A; Shparlinski I, 2023, On some matrix counting problems, http://dx.doi.org/10.48550/arxiv.2310.05038

Garaev M; Rudnick Z; Shparlinski I, 2023, On a family of sparse exponential sums, http://dx.doi.org/10.48550/arxiv.2309.11887

Dartyge C; Martin B; Rivat J; Shparlinski IE; Swaenepoel C, 2023, Reversible primes, http://dx.doi.org/10.48550/arxiv.2309.11380

Bulinski K; Shparlinski IE, 2023, Counting elements of the congruence subgroup, http://dx.doi.org/10.48550/arxiv.2308.10485

Dubickas A; Sha M; Shparlinski IE, 2023, Euclidean minima of algebraic number fields, http://dx.doi.org/10.48550/arxiv.2307.10880

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

Hauck M; Shparlinski IE, 2023, Smooth numbers with few non-zero binary digits, http://dx.doi.org/10.48550/arxiv.2212.10209

Browning T; Shparlinski I, 2023, Square-free values of random polynomials, http://dx.doi.org/10.48550/arxiv.2305.15493

Bulinski K; Ostafe A; Shparlinski IE, 2023, Counting embeddings of free groups into $\mathrm{SL}_2(\mathbb{Z})$ and its subgroups, http://dx.doi.org/10.48550/arxiv.2304.10980

Back to profile page