Skip Navigation


International Mathematics Research Notices Advance Access originally published online on June 25, 2009
International Mathematics Research Notices (2009) 2009:4271-4335, doi:10.1093/imrn/rnp089 published on October 27, 2009
This Article
Right arrow Full Text
Right arrow Full Text (PDF)
Right arrow All Versions of this Article:
2009/22/4271    most recent
rnp089v1
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Right arrow How to cite this article
Google Scholar
Right arrow Articles by Lomelí, L. A.
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© The Author 2009. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org

Functoriality for the Classical Groups over Function Fields

Luis Alberto Lomelí

Department of Mathematics, The University of Iowa, Iowa City, IA 52242, USA

Correspondence: Correspondence to be sent to: llomeli{at}math.uiowa.edu

Langlands' functoriality for generic representations from the split classical groups to an appropriate GLN is established. The functorial lift or transfer to GLN is obtained with the help of a converse theorem once the analytic properties of L-functions are studied using the Langlands–Shahidi approach. This paper is mostly devoted to understanding L-functions for the classical groups over a global function field, since the Langlands–Shahidi method has only been developed over number fields. To overcome many difficulties, stability of {gamma}-factors under twists by highly ramified characters is used together with multiplicativity. Finally, by analyzing the image of functoriality, a proof of the Ramanujan conjecture for generic representations is obtained.

Communicated by Prof. Jim Cogdell


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer: Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.