Are number fields determined by Artin L-Functions ?

Abstract

Let $k$ be a number field, $K/k$ a finite Galois extension with Galois group $G$, $\chi$ a faithful character of $G$. We prove that the Artin L-function $L(s,\chi ,K/k)$ determines the Galois closure of $K$ over $\Q$. In the special case $k=\Q$ it also determines the character $\chi$.

7 pages, change of title