2009 Fiscal Year Final Research Report
On the ring structure of automorphic forms and differential operators
| Project/Area Number |
20740024
|
|---|
| Research Category |
Grant-in-Aid for Young Scientists (B)
|
| Allocation Type | Single-year Grants |
|---|
| Research Field |
Algebra
|
|---|
| Research Institution | Tokyo University of Science |
|---|
Principal Investigator |
青木 宏樹 Tokyo University of Science, 理工学部, 講師 (10333189)
|
|---|
| Project Period (FY) |
2008 – 2009
|
| Keywords | 保型形式 / 微分作用素 / 整数論 |
|---|
| Research Abstract |
Our aim on this project is to determine the structure of automorphic forms by using differential operators. In this two years, we have the following two results :
(1) On the structure of Hilbert modular forms with respect to a real quadratic field with small discriminant, we have a structure theorem when the difference of the weight is small.
(2) On the structure of vector valued Siegel modular forms of degree 2, we have a structure theorem when the discrete subgroup is in a congruent subgroup with a small level.
|
