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 
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     author = {Lucio Guerberoff},
     title = {Period relations for automorphic forms on unitary groups and critical values of $L$-functions},
     journal = {Documenta mathematica},
     pages = {1397--1458},
     year = {2016},
     volume = {21},
     doi = {10.4171/dm/x5},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/x5/}
}
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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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