Subconvexity bounds for triple 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 of the triple L-function. Our method is based on the study of the analytic structure of the corresponding unique trilinear functional on unitary representations of PGL(2,R).

Revised version. To appear in Annals of Math.

Cited by in corpus (1)

• The subconvexity problem for $\GL_{2}$