Artin L-functions to almost monomial Galois groups

Abstract

If $K/\mathbb{Q}$ is a finite Galois extension with an almost monomial Galois group and if $s_0\in \mathbb{C}\setminus \{1\}$ is not a common zero for any two Artin L-functions associated to distinct complex irreducible characters of the Galois group then all Artin L-functions of $K/\mathbb{Q}$ are holomorphic at $s_0$. We present examples and basic properties of almost monomial groups.

6 pages