Subconvexity bounds for triple L-functions and representation theory

We describe a new method to estimate the trilinear period on automorphic representations of PGL₂(R{double-struck}). Such a period gives rise to a special value of the triple Lfunction. 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 PGL₂(R{double-struck}).