Arithmetic of cohomological automorphic representations of orthogonal groups and theta series for indefinite quadratic forms
| Project/Area Number |
17540038
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Algebra
|
|---|
| Research Institution | Keio University |
|---|
Principal Investigator |
MIYAZAKI Takuya Keio University, Faculty of Science and Technology, Associate Professor (10301409)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
ODA Yoshiaki Keio University, Faculty of Science and Technology, Assistant Professor (90325043)
TANAKA Takaaki Keio University, Faculty of Science and Technology, Research Associate (60306850)
HACHIMORI Yoshitaka Tokyo University of Science, Faculty of Science and Technology, Assistant Professor (50433743)
深谷 太香子 慶應義塾大学, 商学部, 講師 (20365464)
|
|---|
| Project Period (FY) |
2005 – 2007
|
| Project Status |
Completed (Fiscal Year 2007)
|
| Budget Amount *help |
¥3,600,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥300,000)
Fiscal Year 2007: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2006: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2005: ¥1,300,000 (Direct Cost: ¥1,300,000)
|
|---|
| Keywords | Degenerate principal series / Eisenstein seeries / zonal polynomial / confluent hypergeometric function / Mellin transform / Rankin-Selberg / Ge enbauer多項式 / 一般型メリン変換 / Rankin-Selber / 斉藤・黒川保型形式 / 実解析的保型形式 / 正規化メリン変換 / 半整数重さ / 留数形式 / 実解析的Siegel保型形式 / 実解析的Eisenstein級数 / Zuckerman導来函手加群 / 合流型超幾何函数 / 退化Whittaker模型 / Maassリフティング / Koecher-Maass級数 / Rankin-Selberg L函数 |
|---|
| Research Abstract |
We construct a kind of real analytic Siegel-Eisenstein series which associate to certain nontempered derived functor module of Sp (2n, R). A close study of its Fourier expansion gives us that the nontrivial Fourier coefficients are supported only for “indefinite" character of the Siegel unipotent subgroup. One can understand this fact to be related to a substancial invariant of the derived functor module, namely, the wave front set of its distribution character.
We also give explicit formula of each Fourier coefficient, which enable us to compute its variously twisted Mellin transform, which give ar generalization of the works of Maass to a special real analytic automorphic representation. As a result we obtain a formula of it written by a Rankin-Selberg type Dirichlet series, where the coefficients include geodesic integrals of Maass wave forms. These study will be applied to construct a nontempered cohomological Saito-Kurokawa representation of Sp (2,A).
|
Report
(4 results)
Research Products
(12 results)
