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On critical values of twisted Artin L-functions

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Abstract

We give a simple proof that critical values of any Artin L-function attached to a representation ϱ with character χ ϱ are stable under twisting by a totally even character χ, up to the dim ϱ-th power of the Gauss sum related to χ and an element in the field generated by the values of χ ϱ and χ over ℚ. This extends a result of Coates and Lichtenbaum as well as the previous work of Ward.

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Correspondence to Peng-Jie Wong.

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Dedicated to the memory of my teacher, Chao-Liang Shen

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Wong, PJ. On critical values of twisted Artin L-functions. Czech Math J 67, 551–555 (2017). https://doi.org/10.21136/CMJ.2017.0134-16

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  • DOI: https://doi.org/10.21136/CMJ.2017.0134-16

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