Boundedness of automorphic 𝐿–functions in vertical strips

Gelbart, Stephen; Shahidi, Freydoon

doi:10.1090/S0894-0347-00-00351-9

Boundedness of automorphic $L$–functions in vertical strips
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by Stephen Gelbart and Freydoon Shahidi;

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

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

Published electronically: 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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