Select Publications

## Preprints

Banks W; Shparlinski IE, 2022, On the greatest common divisor of integer parts of polynomials, http://arxiv.org/abs/2205.00253v1

Kerr B; Shparlinski IE; Wu X; Xi P, 2022, Bounds on bilinear forms with Kloosterman sums, http://arxiv.org/abs/2204.05038v1

Ostafe A; Shparlinski IE, 2022, Integer matrices with a given characteristic polynomial and multiplicative dependence of matrices, http://arxiv.org/abs/2203.03880v2

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://arxiv.org/abs/2110.04657v1

Ostafe A; Shparlinski IE, 2021, Additive energy of cyclic matrix groups and character sums with matrix exponential functions

Baker RC; Chen C; Shparlinski IE, 2021, Large Weyl sums and Hausdorff dimension

Baker RC; Chen C; Shparlinski IE, 2021, Bounds on the Norms of Maximal Operators on Weyl Sums

Shparlinski IE; Thuswaldner JM, 2021, Weyl sums over integers with digital restrictions

Baker RC; Munsch M; Shparlinski IE, 2021, Additive energy and a large sieve inequality for sparse sequences

Kerr B; Shkredov ID; Shparlinski IE; Zaharescu A, 2021, Energy bounds for modular roots and their applications

Ghioca D; Shparlinski I, 2021, Order of torsion for reduction of linearly independent points for a family of Drinfeld modules

Ghioca D; Ostafe A; Saleh S; Shparlinski IE, 2021, On sparsity of representations of polynomials as linear combinations of exponential functions

Ghioca D; Ostafe A; Saleh S; Shparlinski IE, 2020, A sparsity result for the Dynamical Mordell-Lang Conjecture in positive characteristic

Brandes J; Shparlinski IE, 2020, Two-dimensional Weyl sums failing square-root cancellation along lines

Shkredov ID; Shparlinski IE; Zaharescu A, 2020, On the distribution of modular square roots of primes

Mérai L; Shparlinski IE, 2020, On the Dynamical System Generated by the Möbius transformation at Prime Times

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

Shparlinski IE; Wang Q, 2020, Exponential sums with sparse polynomials over finite fields

Ostafe A; Shparlinski I, 2020, On the Skolem problem and some related questions for parametric families of linear recurrence sequences

Konyagin SV; Shparlinski IE; Vyugin IV, 2020, Polynomial Equations in Subgroups and Applications

Kerr B; Mello J; Shparlinski IE, 2020, An effective local--global principle for algebraic varieties and the sum product problem in finite fields

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

Macourt S; Petridis G; Shkredov ID; Shparlinski IE, 2020, Bounds of Trilinear and Trinomial Exponential Sums

Chen C; Shparlinski IE, 2020, Hybrid bounds on two-parametric family Weyl sums along smooth curves

Li R; Shparlinski IE, 2020, Effective bounds on multiplicatively dependent orbits of integer polynomials modulo S-integers

Kerr B; Mérai L; Shparlinski IE, 2020, On digits of Mersenne numbers

Chen C; Shparlinski IE, 2019, Restricted mean value theorems and metric theory of restricted Weyl sums

Dąbrowski A; Pomykała J; Shparlinski IE, 2019, On oracle factoring of integers

Chen C; Shparlinski IE, 2019, On a Hybrid Version of the Vinogradov Mean Value Theorem

Breuer F; Shparlinski IE, 2019, Lower bounds for periods of Ducci sequences

Sha M; Shparlinski IE, 2019, Möbius Randomness Law for Frobenius Traces

Dietmann R; Ostafe A; Shparlinski IE, 2019, Discriminants of Fields Generated by Polynomials of Given Height

Dunn A; Kerr B; Shparlinski IE; Zaharescu A, 2019, Bilinear forms in Weyl sums for modular square roots and applications

Ostafe A; Pottmeyer L; Shparlinski IE, 2019, Perfect powers in value sets and orbits of polynomials

Chen C; Shparlinski IE, 2019, Small values of Weyl sums

Mérai L; Ostafe A; Shparlinski IE, 2019, Dynamical irreducibility of polynomials modulo primes

Mérai L; Shparlinski IE, 2019, Unlikely intersections over finite fields: polynomial orbits in small subgroups

Chen C; Shparlinski IE, 2019, Hausdorff dimension of the large values of Weyl sums

Macourt S; Shparlinski IE, 2019, Double Sums of Kloosterman Sums in Finite Fields

Konyagin SV; Sha M; Shparlinski IE; Stewart CL, 2019, On the distribution of multiplicatively dependent vectors

Chen C; Shparlinski IE, 2019, New bounds of Weyl sums

Shparlinski IE; Technau M, 2019, Kloosterman sums with twice-differentiable functions

de la Bretèche R; Kurlberg P; Shparlinski IE, 2019, On the number of products which form perfect powers and discriminants of multiquadratic extensions

Chen C; Shparlinski IE, 2019, On Large Values of Weyl Sums

Mérai L; Shparlinski IE, 2018, Distribution of short subsequences of inversive congruential pseudorandom numbers modulo $2^t$