Subconvexity bounds for triple L-functions and representation theory

Joseph Bernstein*, Andre Reznikov

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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}).

Original languageEnglish
Pages (from-to)1679-1718
Number of pages40
JournalAnnals of Mathematics
Volume172
Issue number3
DOIs
StatePublished - 2010

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