Boundedness of automorphic -functions in vertical strips

Authors:
Stephen Gelbart and Freydoon Shahidi

Journal:
J. Amer. Math. Soc. **14** (2001), 79-107

MSC (2000):
Primary 11F70, 11R42

DOI:
https://doi.org/10.1090/S0894-0347-00-00351-9

Published electronically:
September 18, 2000

MathSciNet review:
1800349

Full-text PDF

Abstract | References | Similar Articles | Additional Information

In this paper we prove the boundedness in vertical strips of finite width for all the -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:
https://doi.org/10.1090/S0894-0347-00-00351-9

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