Discrepancies in the distribution of Gaussian primes
Number Theory
2025-12-01 v3
Abstract
Motivated by questions of Fouvry and Rudnick on the distribution of Gaussian primes, we develop a very general setting in which one can study inequities in the distribution of analogues of primes through analytic properties of infinitely many -functions. In particular, we give a heuristic argument for the following claim : for more than half of the prime numbers that can be written as a sum of two square, the odd square is the square of a positive integer congruent to .
Keywords
Cite
@article{arxiv.2105.02492,
title = {Discrepancies in the distribution of Gaussian primes},
author = {Lucile Devin},
journal= {arXiv preprint arXiv:2105.02492},
year = {2025}
}
Comments
29 pages, 4 figures, new version after referee's suggestions : changes in the presentation of section 4, appendix added to present pari/gp codes to check for the vanishing at the central point