By Professor Igor Shparlinski

Working Papers

Chen C; Shparlinski IE, 2021, Restricted Mean Value Theorems and the Metric Theory of Restricted Weyl Sums, http://dx.doi.org10.1093/qmath/haaa052

Chen C; Shparlinski IE, 2021, On a hybrid version of the Vinogradov mean value theorem, http://dx.doi.org10.1007/s10474-020-01111-9

Munsch M; Shparlinski IE, 2020, On smooth square-free numbers in arithmetic progressions, http://dx.doi.org10.1112/jlms.12297

Kerr B; Shparlinski IE; Yau KH, 2020, A refinement of the burgess bound for character sums, http://dx.doi.org10.1307/mmj/1573700737

Banks WD; Shparlinski IE, 2020, Sums with the Möbius function twisted by characters with powerful moduli, http://dx.doi.org10.1090/tran/7914

Dąbrowski A; Pomykała J; Shparlinski IE, 2019, On oracle factoring of integers, http://dx.doi.org, http://arxiv.org/abs/1912.00345v4

Konyagin SV; Makarychev SV; Shparlinski IE; Vyugin IV, 2017, On the new bound for the number of solutions of polynomial equations in subgroups and the structure of graphs of Markoff triples, http://dx.doi.org, http://arxiv.org/abs/1711.05335v2

Preprints

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/2404.09295v1

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

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/2310.09052v1

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 subgroups, , http://arxiv.org/abs/2309.10207v1

Bulinski K; Shparlinski IE, 2023, Counting elements of the congruence subgroup, , http://arxiv.org/abs/2308.10485v2

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/2307.07229v1

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

Ostafe A; Shparlinski IE, 2022, Integer matrices with a given characteristic polynomial and multiplicative dependence of matrices, , http://arxiv.org/abs/2203.03880v4

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

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