Fourier optimization, the least quadratic non-residue, and the least prime in an arithmetic progression
Number Theory
2025-08-13 v2 Classical Analysis and ODEs
Abstract
By means of a Fourier optimization framework, we improve the current asymptotic bounds under GRH for two classical problems in number theory: the problem of estimating the least quadratic non-residue modulo a prime, and the problem of estimating the least prime in an arithmetic progression.
Keywords
Cite
@article{arxiv.2404.08380,
title = {Fourier optimization, the least quadratic non-residue, and the least prime in an arithmetic progression},
author = {Emanuel Carneiro and Micah B. Milinovich and Emily Quesada-Herrera and Antonio Pedro Ramos},
journal= {arXiv preprint arXiv:2404.08380},
year = {2025}
}
Comments
33 pages, 3 figures. v2 includes an enhanced numerical discussion in Section 6, and an Appendix