8 papers
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…
Statistics of ranks, determinants and characteristic polynomials of rational matrices
Muhammad Afifurrahman, Vivian Kuperberg, Alina Ostafe +1
We consider the set of matrices with rational entries having numerator and denominator of size at most and obtain upper and lower bounds on the number of such matri…
Estimates for trilinear and quadrilinear character sums
Ãtienne Fouvry, Igor E. Shparlinski, Ping Xi
We obtain new bounds on some trilinear and quadrilinear character sums, which are non-trivial starting from very short ranges of the variables. An application to an apparently new…
Mean value theorems for rational exponential sums
Doowon Koh, Igor E. Shparlinski
We obtain finite field analogues of a series of recent results on various mean value theorems for Weyl sums. Instead of the Vinogradov Mean Value Theorem, our results rest on the c…
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 $Ï(d)=o(\lo…
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…