9 papers · 1 filter
Counting integer matrices with square-free determinants
Alina Ostafe, Igor E. Shparlinski
We consider the set of -matrices with integer elements of size at most and obtain and asymptotic formula on the number of mat…
On Artin's conjecture on average and short character sums
Oleksiy Klurman, Igor E. Shparlinski, Joni Teräväinen
Let denote the number of primes up to for which the integer is a primitive root. We show that satisfies the asymptotic predicted by Artin's conjecture for…
Counting Irreducible polynomials with coefficients from thin subgroups
Alina Ostafe, Igor E. Shparlinski
L. Bary-Soroker and R. Shmueli (2026) have given an asymptotic formula for the number of irreducible polynomials over the finite fields of elements, such that the…
Multiplicative dependence in the denominators of points of elliptic curves
Attila Bérczes, Subham Bhakta, Lajos Hajdu +2
Let be , not necessary distinct, elliptic curves over . We give upper bounds on the frequency of -tuples of points in $E_1(\mathbb{Q})\times \…
Counting solvable -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…
Counting matrices over finite rank multiplicative groups
Aaron Manning, Alina Ostafe, Igor E. Shparlinski
Motivated by recent works on statistics of matrices over sets of number theoretic interest, we study matrices with entries from arbitrary finite subsets of finite rank…