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Boundedness of automorphic $L$-functions in vertical strips

Author(s): Stephen Gelbart; Freydoon Shahidi
Journal: J. Amer. Math. Soc. 14 (2001), 79-107.
MSC (2000): Primary 11F70, 11R42
Posted: September 18, 2000
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Abstract:

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
Email: shahidi@math.purdue.edu

DOI: 10.1090/S0894-0347-00-00351-9
PII: S 0894-0347(00)00351-9
Received by editor(s): December 21, 1999
Received by editor(s) in revised form: June 14, 2000
Posted: 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.
Copyright of article: Copyright 2000, American Mathematical Society

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