A new bound on the relative error in the Chebotarev density theorem
Number Theory
2025-08-14 v2
Abstract
We unconditionally improve the uniformity in the Chebotarev density theorem for Galois extensions of number fields using nonabelian base change. This leads to the first theoretical improvement over Weiss's bound for the least norm of an unramified prime ideal with given Artin symbol.
Keywords
Cite
@article{arxiv.2412.01802,
title = {A new bound on the relative error in the Chebotarev density theorem},
author = {Jesse Thorner and Zhuo Zhang},
journal= {arXiv preprint arXiv:2412.01802},
year = {2025}
}
Comments
34 pages. Significant revisions to exposition in Sections 1 and 2