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 language | English (US) |
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Pages (from-to) | 3695-3724 |
Number of pages | 30 |
Journal | Transactions of the American Mathematical Society |
Volume | 376 |
Issue number | 5 |
DOIs | |
State | Published - 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