Periods, subconvexity of L-functions and representation theory

Abstract

We describe a new method to estimate the trilinear period on automorphic representations of PGL(2,R). Such a period gives rise to a special value of the triple L-function. We prove a bound for the triple period which amounts to a subconvexity bound for the corresponding special value. Our method is based on the study of the analytic structure of the corresponding unique trilinear functional on unitary representations of PGL(2,R).

To appear in J. of Diff. Geometry, Vol. 69 issue 2 in honor of Prof. Raoul Bott; 12 p