Theory of endoscopy for an automorphic representation of a covering group

2016 Fiscal Year Final Research Report

• Project/Area Number: 26610005
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Algebra
• Research Institution: Kyoto University
• Principal Investigator: Ikeda Tamotsu 京都大学, 理学研究科, 教授 (20211716)
• Co-Investigator(Renkei-kenkyūsha): HIRAGA Kaoru 京都大学, 大学院理学研究科, 講師 (10260605)
• Project Period (FY): 2014-04-01 – 2017-03-31
• Keywords: 保型表現 / 保型形式 / 被覆群

Outline of Final Research Achievements

In this research project, we investigated Siegel Eisenstein series defined over a symplectic or a metaplectic group. In particular, we proved the functional equation of a Siegel series. Moreover, by a joint work with Katsurada, we develop a theory of the Gross-Keating invariant of a quadratic form over a non-archimedean local field. As an application, we obtained an explicit formula of a Siegel series.
We also considered the theory of lifting for a symplectic or unitary group defined over a totally real number field. We gave an interesting numerical example for a lifting of Hilbert-Siegel modular forms.

Free Research Field

整数論