On the distribution of modular square roots of primes

Ilya D. Shkredov, Igor E. Shparlinski, Alexandru Zaharescu

Research output: Contribution to journalArticlepeer-review

Abstract

We use recent bounds on bilinear sums with modular square roots to study the distribution of solutions to congruences x2≡p(modq) with primes p⩽P and 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.

Original languageEnglish (US)
Article number43
JournalMathematische Zeitschrift
Volume306
Issue number3
DOIs
StatePublished - Mar 2024

Keywords

  • 11K38
  • 11L07
  • 11L20
  • Modular square roots
  • Prime quadratic residues

ASJC Scopus subject areas

  • General Mathematics

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