GAUSSIAN PHENOMENA FOR SMALL QUADRATIC RESIDUES AND NON-RESIDUES

Debmalya Basak, Kunjakanan Nath, Alexandru Zaharescu

Research output: Contribution to journalArticlepeer-review

Abstract

Assuming the Generalized Riemann Hypothesis, it is known that the smallest quadratic non-residue modulo a prime p is less than or equal to (log p)2. Our aim in this paper is to establish the distribution of quadratic non-residues in even smaller intervals of size (log p)A with A > 1, for almost all primes p.

Original languageEnglish (US)
Pages (from-to)3695-3724
Number of pages30
JournalTransactions of the American Mathematical Society
Volume376
Issue number5
DOIs
StatePublished - May 2023

Keywords

  • Gaussian distribution
  • primes in short intervals
  • quadratic residues and non-residues
  • square-free numbers

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics

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