2006-03-03

Freydoon Shahidi, Purdue University

Stability of Root Numbers with Applications to Functoriality

In order to transfer automorphic forms from classical groups, or more generally reductive groups whose L-groups have classical derived groups, to GL(n) by means of converse theorems applied to appropriate L-functions, one needs to show that the corresponding local root numbers are stable under highly ramified twists. In this talk we discuss the corresponding cases of functoriality and state a general theorem on stability which covers all the cases of functoriality discussed here and does not require any explicit calculations on the group (joint with Cogdell and Piatetski-Shapiro).