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

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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.
Classification : 11F67, 11F70, 11G18, 11R39, 22E55
Keywords: periods, \(L\)-functions, anti-holomorphic cohomology, Deligne's conjecture 
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     author = {Guerberoff, Lucio},
     title = {Period relations for automorphic forms on unitary groups and critical values of {\(L\)-functions}},
     journal = {Documenta mathematica},
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     volume = {21},
     year = {2016},
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     url = {http://geodesic.mathdoc.fr/item/DOCMA_2016__21__a7/}
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Guerberoff, Lucio. Period relations for automorphic forms on unitary groups and critical values of \(L\)-functions. Documenta mathematica, Tome 21 (2016), pp. 1397-1458. http://geodesic.mathdoc.fr/item/DOCMA_2016__21__a7/