Igor E. Shparlinski

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math.NT2025

Multiplicative dependence in the denominators of points of elliptic curves

Attila Bérczes, Subham Bhakta, Lajos Hajdu +2

Let $E_{1}, \dots, E_{s}$ be $s$ , not necessary distinct, elliptic curves over $Q$ . We give upper bounds on the frequency of $s$ -tuples of points in $E_1(\mathbb{Q})\times \…

math.NT2025

Counting solvable $S$ -unit equations and linear recurrence sequences with zeros

Alina Ostafe, Carl Pomerance, Igor E. Shparlinski

We show that only a rather small proportion of linear equations are solvable in elements of a fixed finitely generated subgroup of a multiplicative group of a number field. The arg…

math.NT2025

Multiplicative dependence in linear recurrence sequences

Attila Bérczes, Lajos Hajdu, Alina Ostafe +1

For a wide class of integer linear recurrence sequences $(u (n))_{n = 1}^{\infty}$ , we give an upper bound on the number of $s$ -tuples $\left(n_1, \ldots, n_s\right) \in \lef…

math.NT2024

On Artin's conjecture on average and short character sums

Oleksiy Klurman, Igor E. Shparlinski, Joni Teräväinen

Let $N_{a} (x)$ denote the number of primes up to $x$ for which the integer $a$ is a primitive root. We show that $N_{a} (x)$ satisfies the asymptotic predicted by Artin's conjecture for…

Multiplicative dependence in the denominators of points of elliptic curves

Counting solvable S-unit equations and linear recurrence sequences with zeros

Multiplicative dependence in linear recurrence sequences

On Artin's conjecture on average and short character sums

Counting solvable $S$ -unit equations and linear recurrence sequences with zeros