On an explicit zero-free region for the Dedekind zeta-function

JOURNAL OF NUMBER THEORY

卷:224

Article

Lee, Ethan S.¹ 

[1] UNSW Canberra, Northcott Dr, Canberra, ACT 2612, Australia

关键词: Dedekind zeta-function;    Explicit zero-free region;    Zeros of the Dedekind zeta-function;    Chebotarev density theorem;   

DOI  :  10.1016/j.jnt.2020.12.015

来源: Elsevier

【 摘 要 】

This article establishes new explicit zero-free regions for the Dedekind zeta-function. Two key elements of our proof are a non-negative, even, trigonometric polynomial and explicit upper bounds for the explicit formula of the socalled differenced logarithmic derivative of the Dedekind zeta function. The improvements we establish over the last result of this kind come from two sources. First, our computations use a polynomial which has been optimised by simulated annealing for a similar problem. Second, we establish sharper upper bounds for the aforementioned explicit formula. (c) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free