List of works - Igor Shparlinski

A SPARSITY RESULT FOR THE DYNAMICAL MORDELL–LANG CONJECTURE IN POSITIVE CHARACTERISTIC

scientific article published in 2021

Bilinear forms with exponential sums with binomials

scientific article published in 2018

Bilinear sums of Gauss sums

scientific article published in 2022

Binomial exponential sums

scientific article published in 2020

Bounds of Trilinear and Quadrilinear Exponential Sums

scientific article published in 2019

Bounds of Trilinear and Trinomial Exponential Sums

scientific article published in 2020

Bounds of some double exponential sums

scientific article published in 2021

Bounds on bilinear sums of Kloosterman sums

scientific article published in 2023

Bounds on short character sums and L-functions with characters to a powerful modulus ⬇️

scholarly article

Character sums and deterministic polynomial root finding in finite fields

scientific article published in 2015

Character sums with smooth numbers

scholarly article published on 5 March 2018

Chowla and Sarnak conjectures for Kloosterman sums

scientific article published in 2023

Codes correcting restricted errors

scholarly article

Congruences with intervals and arbitrary sets ⬇️

scholarly article

Density of non-residues in Burgess-type intervals and applications

scientific article published in 2008

Distribution of Farey fractions in residue classes and Lang–Trotter conjectures on average

scientific article published in 2008

Distribution of modular inverses and multiples of small integers and the Sato-Tate conjecture on average

scientific article published in 2008

Double exponential sums with exponential functions

scientific article published in 2017

Double sums of Kloosterman sums in finite fields

scholarly article

Energy bounds, bilinear forms and their applications in function fields

scientific article published in 2022

Estimates for Wieferich numbers

article

Exponential Sums with Sparse Polynomials over Finite Fields

scientific article published in 2021

Exponential sums and rational points on complete intersections

scientific article published in 1990

Exponential sums with Catalan numbers and middle binomial coefficients ⬇️

scholarly article

Identity testing and interpolation from high powers of polynomials of large degree over finite fields

scholarly article

Level curves of rational functions and unimodular points on rational curves ⬇️

scholarly article

Multiplicative Dependence Among Iterated Values of Rational Functions Modulo Finitely Generated Groups

scholarly article

Multiplicative Energy of Shifted Subgroups and Bounds On Exponential Sums with Trinomials in Finite Fields

scientific article published in 2018

Multiplicative congruences with variables from short intervals

scientific article published in 2014

Möbius Randomness Law for Frobenius Traces of Ordinary Curves

scientific article published in 2020

New Bounds of Weyl Sums ⬇️

scholarly article

New estimates for exponential sums over multiplicative subgroups and intervals in prime fields

scientific article published in 2020

ON FINDING SOLUTIONS TO EXPONENTIAL CONGRUENCES

scientific article published in 2018

On Decimations of l-Sequences

scientific article published in 2004

On Distances in Lattices from Algebraic Number Fields

scholarly article

On Multiplicative Dependence of Values of Rational Functions and a Generalization of the Northcott Theorem

scholarly article

On a conjecture of Soundararajan

scientific article published in 2021

On a sum involving the Euler function

scholarly article

On elements of large order on elliptic curves and multiplicative dependent images of rational functions over finite fields

scientific article published in 2021

On smooth square‐free numbers in arithmetic progressions ⬇️

scholarly article

On sparsity of representations of polynomials as linear combinations of exponential functions

scientific article published in 2022

On the Distribution of Orbits of $\mathrm{PGL_2(q)}$ in ${\mathbbF}_{q^n}$ and the Klapper Conjecture

scientific article published in 2010

On the Distribution of Pseudopowers

scientific article published in 2010

On the Glasner property for matrices with polynomial entries

scientific article published in 2022

On the Győry-Sárközy-Stewart conjecture in function fields

scientific article published in 2018

On the Lang-Trotter and Sato-Tate conjectures on average for polynomial families of elliptic curves

scientific article published in 2013

On the Sato–Tate conjecture on average for some families of elliptic curves

scientific article published in 2011

On the exponential large sieve inequality for sparse sequences modulo primes

scientific article published in 2018

On the statistical properties of Diffie-Hellman distributions

scientific article published in 2000

On the typical size and cancellations among the coefficients of some modular forms

scientific article published in 2019

Order of torsion for reduction of linearly independent points for a family of Drinfeld modules

scientific article published in 2022

Orders of Gauss Periods in Finite Fields

Orders of points in families of elliptic curves ⬇️

scholarly article

Period of the power generator and small values of Carmichael's function

Pseudoprime reductions of elliptic curves

scientific article published in 2008

Recurrence Sequences

SMOOTH SQUAREFREE AND SQUAREFULL INTEGERS IN ARITHMETIC PROGRESSIONS ⬇️

scholarly article

Some Divisibility Properties of Binomial Coefficients and the Converse of Wolstenholme's Theorem

scientific article published in 2010

Sparsity of curves and additive and multiplicative expansion of rational maps over finite fields

scholarly article

Sums of algebraic trace functions twisted by arithmetic functions

scientific article published in 2020

The Sato–Tate distribution in thin parametric families of elliptic curves

scholarly article published on 8 March 2018

Trilinear forms with double Kloosterman sums

scholarly article published on 22 August 2018

List of works by Igor Shparlinski

A SPARSITY RESULT FOR THE DYNAMICAL MORDELL–LANG CONJECTURE IN POSITIVE CHARACTERISTIC

Bilinear forms with exponential sums with binomials

Bilinear sums of Gauss sums

Binomial exponential sums

Bounds of Trilinear and Quadrilinear Exponential Sums

Bounds of Trilinear and Trinomial Exponential Sums

Bounds of some double exponential sums

Bounds on bilinear sums of Kloosterman sums

Bounds on short character sums and L-functions with characters to a powerful modulus ⬇️

Character sums and deterministic polynomial root finding in finite fields

Character sums with smooth numbers

Chowla and Sarnak conjectures for Kloosterman sums

Codes correcting restricted errors

Congruences with intervals and arbitrary sets ⬇️

Density of non-residues in Burgess-type intervals and applications

Distribution of Farey fractions in residue classes and Lang–Trotter conjectures on average

Distribution of modular inverses and multiples of small integers and the Sato-Tate conjecture on average

Double exponential sums with exponential functions

Double sums of Kloosterman sums in finite fields

Energy bounds, bilinear forms and their applications in function fields

Estimates for Wieferich numbers

Exponential Sums with Sparse Polynomials over Finite Fields

Exponential sums and rational points on complete intersections

Exponential sums with Catalan numbers and middle binomial coefficients ⬇️

Identity testing and interpolation from high powers of polynomials of large degree over finite fields

Level curves of rational functions and unimodular points on rational curves ⬇️

Multiplicative Dependence Among Iterated Values of Rational Functions Modulo Finitely Generated Groups

Multiplicative Energy of Shifted Subgroups and Bounds On Exponential Sums with Trinomials in Finite Fields

Multiplicative congruences with variables from short intervals

Möbius Randomness Law for Frobenius Traces of Ordinary Curves

New Bounds of Weyl Sums ⬇️

New estimates for exponential sums over multiplicative subgroups and intervals in prime fields

ON FINDING SOLUTIONS TO EXPONENTIAL CONGRUENCES

On Decimations of l-Sequences

On Distances in Lattices from Algebraic Number Fields

On Multiplicative Dependence of Values of Rational Functions and a Generalization of the Northcott Theorem

On a conjecture of Soundararajan

On a sum involving the Euler function

On elements of large order on elliptic curves and multiplicative dependent images of rational functions over finite fields

On smooth square‐free numbers in arithmetic progressions ⬇️

On sparsity of representations of polynomials as linear combinations of exponential functions

On the Distribution of Orbits of $\mathrm{PGL_2(q)}$ in ${\mathbbF}_{q^n}$ and the Klapper Conjecture

On the Distribution of Pseudopowers

On the Glasner property for matrices with polynomial entries

On the Győry-Sárközy-Stewart conjecture in function fields

On the Lang-Trotter and Sato-Tate conjectures on average for polynomial families of elliptic curves

On the Sato–Tate conjecture on average for some families of elliptic curves

On the exponential large sieve inequality for sparse sequences modulo primes

On the statistical properties of Diffie-Hellman distributions

On the typical size and cancellations among the coefficients of some modular forms

Order of torsion for reduction of linearly independent points for a family of Drinfeld modules

Orders of Gauss Periods in Finite Fields

Orders of points in families of elliptic curves ⬇️

Period of the power generator and small values of Carmichael's function

Pseudoprime reductions of elliptic curves

Recurrence Sequences

SMOOTH SQUAREFREE AND SQUAREFULL INTEGERS IN ARITHMETIC PROGRESSIONS ⬇️

Some Divisibility Properties of Binomial Coefficients and the Converse of Wolstenholme's Theorem

Sparsity of curves and additive and multiplicative expansion of rational maps over finite fields

Sums of algebraic trace functions twisted by arithmetic functions

The Sato–Tate distribution in thin parametric families of elliptic curves

Trilinear forms with double Kloosterman sums

Zero testing of p-adic and modular polynomials