Geodesic
On critical values of twisted Artin $L$-functions
Czechoslovak Mathematical Journal, Tome 67 (2017) no. 2, pp. 551-555 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
DOI : 10.21136/CMJ.2017.0134-16
Classification : 11F67, 11F80, 11L05, 11M06
Keywords: Artin $L$-function; character; Galois Gauss sum; special value 
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Wong, Peng-Jie. On critical values of twisted Artin $L$-functions. Czechoslovak Mathematical Journal, Tome 67 (2017) no. 2, pp. 551-555. doi: 10.21136/CMJ.2017.0134-16

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