2003/04/16 by James W. Cogdell, I. I. Piatetski-Shapiro
Mathematics · #math.NT #msc:11F70 #msc:22E55
published as Proceedings of the ICM, Beijing 2002, vol. 2, 119--128
arxiv created 2003/04/16 · arxiv updated 2009/11/30
There has been a recent coming together of the Converse Theorem for \gln and the Langlands-Shahidi method of controlling the analytic properties of automorphic L-functions which has allowed us to establish a number of new cases of functoriality, or the lifting of automorphic forms. In this article we would like to present the current state of the Converse Theorem and outline the method one uses to apply the Converse Theorem to obtain liftings. We will then turn to an exposition of the new liftings and some of their applications.