Langlands functoriality, the converse theorem, and the integral representations of L-functions

Abstract: Langlands functoriality predicts maps between automorphic representations on different groups, dictated by a map of L-groups. One important class of such maps are endoscopic liftings, established by Arthur using the trace formula. In this talk I describe an approach to endoscopic lifting that does not use the trace formula. Instead it follows the approach of Cogdell, Kim, Piatetski-Shapiro and Shahidi, who handled (before Arthur) the case of endoscopic liftings of generic automorphic representations by studying L-functions and using the converse theorem. Using a new integral representations of L-functions of Cai, Friedberg, Ginzburg and Kaplan, I and my collaborators are able to handle all cuspidal automorphic representations, and even to give some liftings outside the work of Arthur.

number theory

Audience: researchers in the topic

Rutgers Number Theory Seminar

Series comments: Seminar talks in this series will be conducted via Zoom. To join our mailing list and/or receive Zoom links and meeting passwords, please email Alexander Walker (alexander.walker@rutgers.edu).