64 citations · 329 across the 206 of their papers we have counts for
17 papers · 1 filter
On the sparsity of non-diagonalisable integer matrices and matrices with a given discriminant
Alina Ostafe, Igor E. Shparlinski
We consider the set of -matrices with integer elements of size at most and obtain upper bounds on the number of matrices from $\mathcal…
Rational numbers with small denominators in short intervals
Igor E. Shparlinski
We use bounds on bilinear forms with Kloosterman fractions and improve the error term in the asymptotic formula of Balazard and Martin (2023) on the average value of the smallest d…
On some matrix counting problems
Ali Mohammadi, Alina Ostafe, Igor Shparlinski
We estimate the frequency of singular matrices and of matrices of a given rank whose entries are parametrised by arbitrary polynomials over the integers and modulo a prime . In…
Number of characteristic polynomials of matrices with bounded height
László Mérai, Igor E. Shparlinski
We consider the set of -matrices with integer elements of size at most and obtain upper and lower bounds on the number of distinct irr…
Reversible primes
Cécile Dartyge, Bruno Martin, Joël Rivat +2
For an -bit positive integer written in binary as where, , , $\vare…
Moments and non-vanishing of -functions over thin subgroups
Marc Munsch, Igor E. Shparlinski
We obtain an asymptotic formula for all moments of Dirichlet -functions modulo when averaged over a subgroup of characters of size with $φ(d)=o(\log p…