Vol. 6, No. 4, 2012

Download this article
Download this article For screen
For printing
Recent Issues

Volume 11, 1 issue

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
Cover
Editorial Board
Editors' Addresses
Editors' Interests
About the Journal
Scientific Advantages
Submission Guidelines
Submission Form
Subscriptions
Editorial Login
Contacts
Author Index
To Appear
 
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Spherical varieties and integral representations of $L$-functions

Yiannis Sakellaridis

Vol. 6 (2012), No. 4, 611–667
Abstract

We present a conceptual and uniform interpretation of the methods of integral representations of L-functions (period integrals, Rankin–Selberg integrals). This leads to (i) a way to classify such integrals, based on the classification of certain embeddings of spherical varieties (whenever the latter is available), (ii) a conjecture that would imply a vast generalization of the method, and (iii) an explanation of the phenomenon of “weight factors” in a relative trace formula. We also prove results of independent interest, such as the generalized Cartan decomposition for spherical varieties of split groups over p-adic fields (following an argument of Gaitsgory and Nadler).

Keywords
automorphic $L$-functions, spherical varieties, Rankin–Selberg, periods of automorphic forms
Mathematical Subject Classification 2000
Primary: 11F67
Secondary: 22E55, 11F70
Milestones
Received: 31 March 2010
Revised: 4 July 2011
Accepted: 1 August 2011
Published: 25 July 2012
Authors
Yiannis Sakellaridis
Department of Mathematics and Computer Science
Rutgers University
101 Warren Street
Smith Hall 216
Newark, NJ 07102
United States