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

TL;DR

This paper establishes new explicit zero-free regions for Dedekind zeta-functions of number fields, refining previous bounds and extending results to all fields, especially for low-lying zeros.

Contribution

It provides improved and explicit zero-free regions for Dedekind zeta-functions, extending Kadiri's results to all number fields and refining constants.

Findings

New explicit zero-free regions for Dedekind zeta-functions

Extension of Kadiri's results to all number fields

Improved constants for low-lying zeros

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.