Subconvexity bounds for triple L-functions and representation theory

• 成果类型: Article
• 署名作者: Bernstein, Joseph; Reznikov, Andre
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2010.172.1679
• 发表日期: 2010
• 页码: 1679-1718
• 关键词: trilinear forms; fourier coefficients; EXTENSIONS

摘要

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).