Subconvexity bounds for triple L-functions and representation theory

Details Subconvexity bounds for triple L-functions and representation theory Subconvexity bounds for triple L-functions and representation theory

2006-08-22

arxiv.org/abs/math/0608555v3

Mathematics

Number Theory

Revised version. To appear in Annals of Math.

Scientific paper

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).

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