Estimates of automorphic functions

2003/05/25 by Joseph Bernstein, Bernstein, Joseph, Andre Reznikov +2 · 2 citations
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT) #Representation Theory (math.RT) #math.NT #math.RT

paper · pdf · doi:10.48550/arxiv.math/0305351

21 pages, to appear in special issue of Moscow Math. J. in honor of Pierre Cartier

openalex publication_date 2003/05/25 · arxiv created 2003/06/12 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a new method of estimating trilinear period for automorphic representations of SL(2,R). The method is based on the uniqueness principle in representation theory. We show how to separate the exponentially decaying factor in the triple period from the essential automorphic factor which behaves polynomially. We also describe a general method which gives an estimate on the average of the automorphic factor and thus prove a convexity bound for the triple period.

Cited by

• Remarks on a triple integral
• Norms of geodesic restrictions for eigenfunctions on hyperbolic surfaces and representation theory

Related

• Periods, subconvexity of L-functions and representation theory
• Subconvexity bounds for triple L-functions and representation theory
• Automorphic SL₂-periods and the subconvexity problem for GL₂ × GL₃
• On Period Relations for Automorphic L-functions I
• Elements of Automorphic Representations