Boundedness of automorphic 𝐿–functions in vertical strips

Abstract

In this paper we prove the boundedness in vertical strips of finite width for all the L 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.