2011 Fiscal Year Final Research Report
Study on spherical functions on Lie groups and automorphic L-functions
| Project/Area Number |
21740028
|
|---|
| Research Category |
Grant-in-Aid for Young Scientists (B)
|
| Allocation Type | Single-year Grants |
|---|
| Research Field |
Algebra
|
|---|
| Research Institution | Seikei University |
|---|
Principal Investigator |
ISHII Taku 成蹊大学, 理工学部, 准教授 (60406650)
|
|---|
| Project Period (FY) |
2009 – 2011
|
| Keywords | 保型形式 / 保型 L 関数 / Rankin-Selberg 法 / Whittaker 模型 / Whittaker 関数 / 主系列表現 |
|---|
| Research Abstract |
The aim of our study is to establish fundamental results on zeta functions for automorphic forms (automorphic L-functions) such as the analytic continuations and the functional equations, through their integral representations (zeta integrals). Using explicit formulas for generalized spherical functions, that is, special functions appearing in the Fourier expansions of automorphic forms, we have computed archimedean zeta integrals. Especially we calculate the archimedean zeta integrals for the L-functions on SO(2n+1)×GL(m) and the standard L-function on GL(3) and obtained the local and the global functional equations.
|
