A Refined Conjecture for the Variance of Gaussian Primes Across Sectors
Number Theory
2021-02-24 v3
Abstract
We derive a refined conjecture for the variance of Gaussian primes across sectors, with a power saving error term, by applying the L-functions Ratios Conjecture. We observe a bifurcation point in the main term, consistent with the Random Matrix Theory (RMT) heuristic previously proposed by Rudnick and Waxman. Our model also identifies a second bifurcation point, undetected by the RMT model, that emerges upon taking into account lower order terms. For sufficiently small sectors, we moreover prove an unconditional result that is consistent with our conjecture down to lower order terms.
Keywords
Cite
@article{arxiv.1901.07386,
title = {A Refined Conjecture for the Variance of Gaussian Primes Across Sectors},
author = {Ryan C. Chen and Yujin H. Kim and Jared D. Lichtman and Steven J. Miller and Alina Shubina and Shannon Sweitzer and Ezra Waxman and Eric Winsor and Jianing Yang},
journal= {arXiv preprint arXiv:1901.07386},
year = {2021}
}
Comments
47 pages. Minor revisions. Appendix with relevant Mathematica code, included. Accepted for publication in Experimental Mathematics