Periods, subconvexity of L-functions and representation theory

Research paper by Joseph Bernstein, Andre Reznikov

Indexed on: 20 Apr '05Published on: 20 Apr '05Published in: Mathematics - Representation Theory


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).