Czechoslovak Mathematical Journal, Vol. 67, No. 2, pp. 551-555, 2017

On critical values of twisted Artin $L$-functions

Peng-Jie Wong

Received March 18, 2016.  First published March 28, 2017.

Abstract:  We give a simple proof that critical values of any Artin $L$-function attached to a representation $\rho$ with character $\chi_{\rho}$ are stable under twisting by a totally even character $\chi$, up to the $\dim\rho$-th power of the Gauss sum related to $\chi$ and an element in the field generated by the values of $\chi_{\rho}$ and $\chi$ over $\mathbb{Q}$. This extends a result of Coates and Lichtenbaum as well as the previous work of Ward.
Keywords:  Artin $L$-function; character; Galois Gauss sum; special value
Classification MSC:  11F67, 11F80, 11L05, 11M06
DOI:  10.21136/CMJ.2017.0134-16

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Affiliations:   Peng-Jie Wong, Department of Mathematics and Statistics, Queen's University, Jeffery Hall, 48 University Ave., Kingston, K7L 3N6, Ontario, Canada, e-mail:

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