Subconvexity bounds for tripleL-functions and representation theory

2010/10/05 by Joseph Bernstein, André Reznikov · 1 citation
Mathematics · #Advanced Algebra and Geometry #Mathematical Analysis and Transform Methods #Finite Group Theory Research #Mathematics #Representation (politics) #Humanities #Algebra over a field #Pure mathematics #Combinatorics #Art

paper · pdf · doi:10.4007/annals.2010.172.1679

openalex publication_date 2010/10/05 · openalex created_date 2016/06/24 · openalex updated_date 2026/06/11

Abstract

We describe a new method to estimate the trilinear period on automorphic representations of PGL 2 ./. 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 PGL 2 ./.

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