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

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.

References in corpus (4)

• Local-global compatibility and the action of monodromy on nearby cycles
• Period relations for automorphic induction and applications, I
• On some arithmetic properties of automorphic forms of GL(m) over a division algebra
• Period relations for automorphic forms on unitary groups and critical values of $L$-functions

Cited by in corpus (3)

• Deligne's conjecture for automorphic motives over CM-fields
• Automorphic Forms on Unitary Groups
• Factorization of arithmetic automorphic periods