Values of twisted Artin $L$-functions

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 an element generated over $\mathbb Q$ by the values of $χ$ and $χ_ρ$, and a product with a power of the Gauss sum $τ(χ)$ equal to the dimension of $ρ$. This extends a result due to J. Coates and S. Lichtenbaum.

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