Vol. 6, No. 4, 2012

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

Volume 12
Issue 7, 1559–1821
Issue 6, 1311–1557
Issue 5, 1001–1309
Issue 4, 751–999
Issue 3, 493–750
Issue 2, 227–492
Issue 1, 1–225

Volume 11, 10 issues

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
About the Journal
Editorial Board
Editors' Addresses
Editors' Interests
Scientific Advantages
Submission Guidelines
Submission Form
Editorial Login
Ethics Statement
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

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).

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