On the Semigroup of Artin's L-functions holomorphic at $s_0$. II

TL;DR

This paper introduces two new criteria to determine when Artin L-functions are holomorphic at a specific complex point, enhancing understanding of their analytic properties in Galois extensions.

Contribution

It provides novel criteria for the holomorphy of Artin L-functions at a given point, advancing the theoretical framework in number theory.

Findings

Two new criteria for holomorphy of Artin L-functions at $s_0$

Improved understanding of the semigroup structure of these L-functions

Potential implications for Galois representations and number theory

Abstract

Let $K/{\mathbb Q}$ be a finite Galois extension, and let $s_0\neq 1$ be a complex number. We present two new criteria for the Artin L-functions to be holomorphic at $s_0$.