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arXiv · 1401.4296

Values of twisted Artin $L$-functions

Kenneth Ward
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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.

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Kenneth Ward. 2014-01-17. Values of twisted Artin $L$-functions. https://doi.org/10.1007/s00013-014-0692-7

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