Period Relations for Automorphic Forms on Unitary Groups and Critical Values of L-Functions

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.

2010 Mathematics Subject Classification: 11F67 (Primary) 11F70, 11G18, 11R39, 22E55 (Secondary).

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