L-functions and theta correspondence for classical groups

• 成果类型: Article
• 署名作者: Yamana, Shunsuke
• 署名单位: Kyushu University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-013-0476-x
• 发表日期: 2014
• 页码: 651-732
• 关键词: degenerate principal series; siegel-weil formula; howe correspondence; eisenstein series; REPRESENTATIONS; dichotomy; poles; INTEGRALS; q)

摘要

Using the doubling method of Piatetski-Shapiro and Rallis, we develop a theory of local factors of representations of classical groups and apply it to give a necessary and sufficient condition for nonvanishing of global theta liftings in terms of analytic properties of the L-functions and local theta correspondence.