Period relations for automorphic forms on unitary groups and critical values of $L$-functions

Abstract

In this paper we explore some properties of periods attached to automorphic representations of unitary groups over CM fields and the critical values of their $L$-functions. We prove a formula expressing the critical values in the range of absolute convergence in terms of Petersson norms of holomorphic automorphic forms. On the other hand, we express the Deligne period of a related motive as a product of quadratic periods and compare the two expressions by means of Deligne's conjecture.

51 pages; incorporated referee comments

Cited by in corpus (5)

• Galois equivariance of critical values of $L$-functions for unitary groups
• Automorphic Forms on Unitary Groups
• On finiteness theorems for automorphic forms
• Factorization of arithmetic automorphic periods
• On critical values of L-functions of potentially automorphic motives