Geodesic
Period relations for automorphic forms on unitary groups and critical values of $L$-functions
Documenta mathematica, Tome 21 (2016), pp. 1397-1458

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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.
DOI : 10.4171/dm/x5
Classification : 11F67, 11F70, 11G18, 11R39, 22E55
Mots-clés : L-functions, periods, Deligne's conjecture, anti-holomorphic cohomology 
Lucio Guerberoff. Period relations for automorphic forms on unitary groups and critical values of $L$-functions. Documenta mathematica, Tome 21 (2016), pp. 1397-1458. doi: 10.4171/dm/x5
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     title = {Period relations for automorphic forms on unitary groups and critical values of $L$-functions},
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