The regularized Siegel-Weil formula (the second term identity) and the Rallis inner product formula

• 成果类型: Article
• 署名作者: Gan, Wee Teck; Qiu, Yannan; Takeda, Shuichiro
• 署名单位: National University of Singapore; University of Missouri System; University of Missouri Columbia
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-014-0509-0
• 发表日期: 2014
• 页码: 739-831
• 关键词: degenerate principal series; automorphic-forms; eisenstein series; REPRESENTATIONS; dichotomy; liftings; poles

摘要

In this paper, we establish the second term identity of the Siegel-Weil formula in full generality, and derive the Rallis inner product formula for global theta lifts for any dual pair. As a corollary, we resolve the non-vanishing problem of global theta lifts initiated by Steve Rallis.