On the distribution of modular square roots of primes

2020/09/08 by Ilya D. Shkredov, Shkredov, Ilya D., Igor E. Shparlinski +3
Mathematics · #Analytic Number Theory Research #FOS: Mathematics #History and Theory of Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2009.03460

openalex publication_date 2020/09/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We use recent bounds on bilinear sums with modular square roots to study the distribution of solutions to congruences x² ≡ p \pmod q with primes p≤ P and integers q ≤ 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.

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