Vol. 260, No. 2, 2012

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 327: 1
Vol. 326: 1  2
Vol. 325: 1  2
Vol. 324: 1  2
Vol. 323: 1  2
Vol. 322: 1  2
Vol. 321: 1  2
Vol. 320: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Subscriptions
Editorial Board
Officers
Contacts
 
Submission Guidelines
Submission Form
Policies for Authors
 
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
 
Other MSP Journals
The functional equation and beyond endoscopy

P. Edward Herman

Vol. 260 (2012), No. 2, 497–513
Abstract

In his paper “Beyond endoscopy,” Langlands tries to understand functoriality via poles of L-functions. This paper further investigates the analytic continuation of an L-function associated to a GL2 automorphic form through the trace formula. Though the usual way to obtain the analytic continuation of an L-function is through its functional equation, this paper shows that by simply assuming the trace formula, the functional equation of the L-function may be recovered. This paper is a step towards understanding the analytic continuation of the L-function at the same time as capturing information about functoriality.

From the perspective of analytic number theory, obtaining the functional equation from the trace formula implies that Voronoi summation should in general be also a consequence of the trace formula.

Keywords
trace formula, L-functions, functional equation, automorphic forms
Mathematical Subject Classification 2010
Primary: 11F12, 11F66, 11F72, 11L05
Milestones
Received: 1 August 2012
Accepted: 27 September 2012
Published: 30 November 2012
Authors
P. Edward Herman
Department of Mathematics
University of Chicago
5734 S. University Avenue
Chicago, IL 60637
United States