Doubling constructions and tensor product L-functions: the linear case

• 成果类型: Article
• 署名作者: Cai, Yuanqing; Friedberg, Solomon; Ginzburg, David; Kaplan, Eyal
• 署名单位: Boston College; Weizmann Institute of Science; Tel Aviv University; Bar Ilan University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-019-00883-4
• 发表日期: 2019
• 页码: 985-1068
• 关键词: rankin-selberg integrals; p-adic groups; unramified principal series; induced representations; residual spectrum; classical-groups; bessel models; gamma-factors; THEOREM; functoriality

摘要

We present an integral representation for the tensor product L-function of a pair of automorphic cuspidal representations, one of a classical group, the other of a general linear group. Our construction is uniform over all classical groups, and is applicable to all cuspidal representations; it does not require genericity. The main new ideas of the construction are the use of generalized Speh representations as inducing data for the Eisenstein series and the introduction of a new (global and local) model, which generalizes the Whittaker model. Here we consider linear groups, but our construction also extends to arbitrary degree metaplectic coverings; this will be the topic of an upcoming work.