The least prime ideal in the Chebotarev Density Theorem
Number Theory
2019-02-26 v1
Abstract
In this article, we prove a new bound for the least prime ideal in the Chebotarev density theorem, which improves the main theorem of Zaman [Funct. Approx. Comment. Math. 57 (2017), no.1, 115-142] by a factor of . Our main improvement comes from a new version of Tur\'an's power sum method. The key new idea is to use Harnack's inequality for harmonic functions to derive a superior lower bound for the generalised Fej\'er kernel.
Keywords
Cite
@article{arxiv.1902.08640,
title = {The least prime ideal in the Chebotarev Density Theorem},
author = {Habiba Kadiri and Nathan Ng and Peng-Jie Wong},
journal= {arXiv preprint arXiv:1902.08640},
year = {2019}
}
Comments
Published online in the Proceedings of the AMS