Vol. 7, No. 1, 2013

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

Volume 10
Issue 9, 1845–2052
Issue 8, 1601–1843
Issue 7, 1373–1600
Issue 6, 1147–1371
Issue 5, 939–1146
Issue 4, 695–938
Issue 3, 451–694
Issue 2, 215–450
Issue 1, 1–214

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)
$L$-functions and periods of adjoint motives

Michael Harris

Vol. 7 (2013), No. 1, 117–155
Abstract

The article studies the compatibility of the refined Gross–Prasad (or Ichino–Ikeda) conjecture for unitary groups, due to Neal Harris, with Deligne’s conjecture on critical values of L-functions. When the automorphic representations are of motivic type, it is shown that the L-values that arise in the formula are critical in Deligne’s sense, and their Deligne periods can be written explicitly as products of Petersson norms of arithmetically normalized coherent cohomology classes. In some cases this can be used to verify Deligne’s conjecture for critical values of adjoint type (Asai) L-functions.

Keywords
adjoint $L$-functions, automorphic forms, motives, Ichino–Ikeda conjecture, periods
Mathematical Subject Classification 2010
Primary: 11F67
Secondary: 11F70, 14G35, 11G09
Milestones
Received: 10 July 2011
Revised: 12 October 2011
Accepted: 20 February 2012
Published: 28 March 2013
Authors
Michael Harris
Tour 15-25, 4ème étage, bureau 420
Institut de Mathématiques de Jussieu
4, place Jussieu
75252 Paris CEDEX 05
France
http://people.math.jussieu.fr/~harris/