On the $q$-analogue of the pair correlation conjecture via Fourier optimization
Number Theory
2023-02-17 v2 Classical Analysis and ODEs
Abstract
We study the -analogue of the average of Montgomery's function over bounded intervals. Assuming the Generalized Riemann Hypothesis for Dirichlet -functions, we obtain upper and lower bounds for this average over an interval that are quite close to the pointwise conjectured value of 1. To compute our bounds, we extend a Fourier analysis approach by Carneiro, Chandee, Chirre, and Milinovich, and apply computational methods of non-smooth programming.
Keywords
Cite
@article{arxiv.2108.10238,
title = {On the $q$-analogue of the pair correlation conjecture via Fourier optimization},
author = {Emily Quesada-Herrera},
journal= {arXiv preprint arXiv:2108.10238},
year = {2023}
}
Comments
17 pages, 3 figures. Minor edits. To appear in Math. Comp