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arXiv · 2002.05456

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

Ethan S. Lee
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Abstract

We establish 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 so-called 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.

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Ethan S. Lee. 2020-02-13. On an explicit zero-free region for the Dedekind zeta-function. https://doi.org/10.1016/j.jnt.2020.12.015

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