Poisson Behavior for Chains of Small Quadratic Non-Residues

Debmalya Basak, Kunjakanan Nath, Alexandru Zaharescu

Research output: Contribution to journalArticlepeer-review


It is known that under the Generalized Riemann Hypothesis, the smallest quadratic non-residue modulo a prime p is less than or equal to (log p)2. In ranges slightly larger, of size (log p)A with A > 2, we consider chains of r consecutive quadratic non-residues. We prove unconditionally that for almost all primes p in short intervals, these chains exhibit Poisson behavior.

Original languageEnglish (US)
Article numberrnad168
Pages (from-to)3356-3390
Number of pages35
JournalInternational Mathematics Research Notices
Issue number4
StatePublished - Feb 1 2024

ASJC Scopus subject areas

  • General Mathematics


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