On the distribution of modular square roots of primes

Abstract

We use recent bounds on bilinear sums with modular square roots to study the distribution of solutions to congruences $x^2\equiv p(\mathrm{mod}q)$ with primes $p\le P$ and integers $q\le Q$. This can be considered as a combined scenario of Duke, Friedlander and Iwaniec with averaging only over the modulus $q$ and of Dunn, Kerr, Shparlinski and Zaharescu with averaging only over $p$.

Cited by in corpus (1)

• Energy bounds for modular roots and their applications