On the distribution of modular square roots of primes

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

doi:10.1007/s00209-024-03436-5

On the distribution of modular square roots of primes

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

Mathematics

Research output: Contribution to journal › Article › peer-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 language	English (US)
Article number	43
Journal	Mathematische Zeitschrift
Volume	306
Issue number	3
Early online date	Feb 10 2024
DOIs	https://doi.org/10.1007/s00209-024-03436-5
State	Published - Mar 2024

Keywords

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

ASJC Scopus subject areas

General Mathematics

Online availability

10.1007/s00209-024-03436-5License: CC BY

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AU - Zaharescu, Alexandru

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AB - 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.

KW - 11K38

KW - 11L07

KW - 11L20

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KW - Prime quadratic residues

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JO - Mathematische Zeitschrift

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ER -

On the distribution of modular square roots of primes

Abstract

Keywords

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