English

On the distribution of modular square roots of primes

Number Theory 2020-09-09 v1

Abstract

We use recent bounds on bilinear sums with modular square roots to study the distribution of solutions to congruences x2p(modq)x^2 \equiv p \pmod q with primes pPp\le P and integers qQq \le Q. This can be considered as a combined scenario of Duke, Friedlander and Iwaniec with averaging only over the modulus qq and of Dunn, Kerr, Shparlinski and Zaharescu with averaging only over pp.

Keywords

Cite

@article{arxiv.2009.03460,
  title  = {On the distribution of modular square roots of primes},
  author = {Ilya D. Shkredov and Igor E. Shparlinski and Alexandru Zaharescu},
  journal= {arXiv preprint arXiv:2009.03460},
  year   = {2020}
}