2010 Fiscal Year Final Research Report
The Research for Eisenstein series and applications
| Project/Area Number |
21840044
|
|---|
| Research Category |
Grant-in-Aid for Research Activity Start-up
|
| Allocation Type | Single-year Grants |
|---|
| Research Field |
Algebra
|
|---|
| Research Institution | Chiba Institute of Technology |
|---|
Principal Investigator |
GUNJI Keiichi Chiba Institute of Technology, 工学, 助教 (00550659)
|
|---|
| Project Period (FY) |
2009 – 2010
|
| Keywords | 整数論 / Siegel保型形式 / Eisenstein級数 |
|---|
| Research Abstract |
There are two main result in our research ; one is the geometric application, and the other is the relationship to Siegel-Weil formula. For the geometric application, we calculate the constant term of the Siegel-Eisenstein series of weight g+1 and degree g, which allows us to calculate a part of the cohomology of the modular varieties. On Siege-Weil formula, we can show that the Siegel-Eisenstein series of degree 2, weight 2, and level p (prime) coincide with the genus theta series, which is the average of the theta series. Such result is the important example of the Siegel-Weil formula for low weights.
|
