Subconvexity bounds for triple L-functions and representation theory

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Abstract

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}). © 2010 by Princeton University (Mathematics Department).

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Bernstein, J., & Reznikov, A. (2010). Subconvexity bounds for triple L-functions and representation theory. Annals of Mathematics, 172(3), 1679–1718. https://doi.org/10.4007/annals.2010.172.1679

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