Values of twisted Artin L-functions

摘要

This note gives a simple proof that certain values of Artin’s L-function, for a representation ρ with character χ_ρ, are stable under twisting by an even Dirichlet character χ, up to the dim(ρ)th power of the Gauss sum τ (χ) and an element generated over Q by the values of χ and χ_ρ. This extends a result due to J. Coates and S. Lichtenbaum.