Values of twisted Artin $L$-functions

Abstract

This note gives a simple proof that certain values of Artin's $L$-function, for a representation $\rho$ with character ${\chi }_{\rho }$, are stable under twisting by an even Dirichlet character $\chi$, up to an element generated over $\mathbb{Q}$ by the values of $\chi$ and ${\chi }_{\rho }$, and a product with a power of the Gauss sum $\tau (\chi )$ equal to the dimension of $\rho$. This extends a result due to J. Coates and S. Lichtenbaum.

arXiv comment6 pages