Kenneth Ward
Published 2014-01-17, updated 2014-09-11Version 2
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.
Comments: 6 pages. minor changes. To appear in Archiv der Mathematik (2014)
A converse to a theorem of Gauss on Gauss sums
On a generalization of Menon-Sury identity to number fields involving a Dirichlet Character
Families Of Elliptic Curves With The Same Mod 8 Representations
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