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arXiv · 2506.19319

New zero-free regions for Dedekind zeta-functions at small and large ordinates

Sourabhashis Das·Swati Gaba·Ethan Simpson Lee·Aditi Savalia·Peng-Jie Wong
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Abstract

Given a number field $L\neq \mathbb{Q}$, we obtain new and explicit zero-free regions for Dedekind zeta-functions of $L$, which refine the previous works of Ahn--Kwon, Kadiri, and Lee. In particular, for low-lying zeros, we extend Kadiri's result to all number fields while improving the main constant.

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Sourabhashis Das, Swati Gaba, Ethan Simpson Lee, Aditi Savalia, Peng-Jie Wong. 2025-06-24. New zero-free regions for Dedekind zeta-functions at small and large ordinates. https://arxiv.org/abs/2506.19319

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