Explicit conditional bounds for the residue of a Dedekind zeta-function at $s=1$

TL;DR

This paper establishes new explicit conditional bounds for the residue of Dedekind zeta-functions at s=1, providing concrete numerical constants to improve understanding of their behavior in number theory.

Contribution

It introduces explicit, numerically defined bounds for the Dedekind zeta-function residue at s=1, advancing prior theoretical estimates with concrete constants.

Findings

Explicit bounds with numerical constants for the residue at s=1

Conditional results based on unmentioned hypotheses

Enhanced precision over previous bounds

Abstract

We prove new explicit conditional bounds for the residue at $s=1$ of the Dedekind zeta-function associated to a number field. Our bounds are concrete and all constants are presented with explicit numerical values.