Galois equivariance of critical values of $L$-functions for unitary groups

Lucio Guerberoff; Jie Lin

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arXiv · 1612.09590

Galois equivariance of critical values of $L$-functions for unitary groups

Lucio Guerberoff·Jie Lin

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Abstract

The goal of this paper is to provide a refinement of a formula proved by the first author which expresses some critical values of automorphic $L$-functions on unitary groups as Petersson norms of automorphic forms. Here we provide a Galois equivariant version of the formula. We also give some applications to special values of automorphic representations of $\GL_{n}\times\GL_{1}$. We show that our results are compatible with Deligne's conjecture.

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Lucio Guerberoff, Jie Lin. 2016-12-30. Galois equivariance of critical values of $L$-functions for unitary groups. https://arxiv.org/abs/1612.09590

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