Doubling constructions: Global functoriality for non-generic cuspidal representations

• 成果类型: Article
• 署名作者: Cai, Yuanqing; Friedberg, Solomon; Kaplan, Eyal
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2024.200.3.2
• 发表日期: 2024
• 页码: 893-966
• 关键词: product l-functions; automorphic-forms; euler products; series; CLASSIFICATION; coefficients; functionals; uniqueness; INTEGRALS; THEOREM

摘要

We study the generalized doubling method for pairs of representations of G x GLk where G is a symplectic group, split special orthogonal group or split general spin group. We analyze the poles of the local integrals and prove that the global completed L-function with a cuspidal representation of GLk twisted by a highly ramified Hecke character is entire. We obtain a new proof of the weak functorial transfer of cuspidal automorphic representations of G to the natural general linear group, which is independent of the trace formula and its prerequisites, by combining our results with the Converse Theorem.