On holomorphic Artin L-functions

Abstract

Let $K/\mathbb{Q}$ be a finite Galois extension, $s_0\in \mathbb{C}\setminus \{1\}$, $Hol(s_0)$ the semigroup of Artin L-functions holomorphic at $s_0$. If the Galois group is almost monomial then Artin's L-functions are holomorphic at $s_0$ if and only if $Hol(s_0)$ is factorial. This holds also if $s_0$ is a zero of an irreducible L-function of dimension $\le 2$, without any condition on the Galois group.

arXiv comment6 pages, correction to the definition of an almost monomial group