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Boundedness of automorphic $L$-functions in vertical strips

Authors: Stephen Gelbart and Freydoon Shahidi
Journal: J. Amer. Math. Soc. 14 (2001), 79-107
MSC (2000): Primary 11F70, 11R42
Published electronically: September 18, 2000
MathSciNet review: 1800349
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In this paper we prove the boundedness in vertical strips of finite width for all the $L$-functions that appear in constant terms of Eisenstein series, under a certain natural assumption on local normalized intertwining operators. This result has been quite important in establishing recent cases of Langlands functoriality by Cogdell, Kim, Piatetski-Shapiro, and Shahidi, using converse theorems.

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Additional Information

Stephen Gelbart
Affiliation: Nicki and J. Ira Harris Professorial Chair, Weizmann Institute of Science, Rehovot 76100, Israel

Freydoon Shahidi
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907

Received by editor(s): December 21, 1999
Received by editor(s) in revised form: June 14, 2000
Published electronically: September 18, 2000
Additional Notes: The first author was partially supported by a Minerva Grant.
The second author was partially supported by NSF Grant DMS–9970156.
Article copyright: © Copyright 2000 American Mathematical Society

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