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P-Adic and analytic properties of period integrals and values of L-functions

Content Provider	Springer Nature Link
Author	Harris, Michael
Copyright Year	2016
Abstract	The Ichino-Ikeda conjecture is an identity that relates a ratio of special values of automorphic L-functions to a ratio of period integrals. Both sides of this identity are expected to satisfy certain equidistribution properties when the data vary, and indeed it has been possible to transfer such properties from one side of the identity to the other in cases where the identity is known. The present article studies parallels between complex-analytic and p-adic equidistribution properties and relates the latter to questions about Galois cohomology.La conjecture d’Ichino-Ikeda est une identité qui met en relation un rapport entre valeurs spéciales de fonctions L automorphes et un rapport entre périodes d’intégrales. On attend à ce que les deux côtés de cette identité vérifient certaines propriétés d’équidistribution lorsqu’on fait varier les données ; en effet, dans certains cas on a réussi à transférer de telles propriétés d’un côté de l’identité à l’autre. Cet article développe des parallèles entre les propriétés d’équidistribution dans le cadre complexe-analytique et dans le cadre p-adique; dans la situation p-adique ces propriétés sont liées à des questions sur la cohomologie galoisienne.
Starting Page	435
Ending Page	452
Page Count	18
File Format	PDF
ISSN	21954755
Journal	Annales mathématiques du Québec
Volume Number	40
Issue Number	2
e-ISSN	21954763
Language	English
Publisher	Springer International Publishing
Publisher Date	2016-02-17
Publisher Place	Cham
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Galois representations Special values of automorphic $L$-series, periods of modular forms, cohomology, modular symbols Algebra Galois representation Analysis Shimura variety Mathematics Number Theory Special values of L-functions Representation-theoretic methods; automorphic representations over local and global fields Arithmetic aspects of modular and Shimura varieties
Content Type	Text
Resource Type	Article
Subject	Mathematics

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