English

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

R2 v1 2026-06-28T20:20:14.671Z