12/13/2004

Andre Reznikov
Bar-Ilan University

Subconvexity bound for triple L-function and representation theory

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