1998 Fiscal Year Final Research Report Summary
Investigation of Eisenstein series on bounded symmeric domain
| Project/Area Number |
09640002
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Algebra
|
|---|
| Research Institution | Muroran Institut of Technology |
|---|
Principal Investigator |
KATSURADA Hidenori Muroran Institute of Technology, Professor, 工学部, 教授 (80133792)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
CHIGIRA Naoki Muroran Institute of Technology, Associate Professor, 工学部, 助教授 (40292073)
SATO Motohiko Muroran Institute of Technology, Associate Professor, 工学部, 助教授 (30254139)
TAKEGAHARA Yugen Muroran Institute of Technology, Associate Professor, 工学部, 助教授 (10211351)
|
|---|
| Project Period (FY) |
1997 – 1998
|
| Keywords | Eisenstein series / Siegel series / Fourier coefficients / Maass zeta function / Squared Moebius function / Local density |
|---|
| Research Abstract |
1. We gave an explicit formula for the Siegel series on any local field (partly with T.Watanabe). As a result, we gave an explicit formula for the Fourier coefficient of the Siegel-Eisenstein series. In particular, we made a table of Fourier coefficients of Siegel-Bisenstein series of degree 3 (with S.Sugawara).
2. Using the result of 1 we determined a 'good' Euler factor of a zeta function of Andrianov type for the Siegel- Eisenstein series.
3 We gave a simpler proof to the induction formula for Siegel series by Y.Kitaoka and P.Feit.
4. On the set of integral quadratic forms, we defined an analogue of the square of the usual Moebius function, which we call squared Moebius function.
5. We related the Kocher-Maass zeta function for a Siegel modular form in terms of the standard zeta function for it and the squared Moebius function. As a result, we gave an explicit form of the Maass zeta function for the Klingen-Eisenstein lift of a cusp form of one variable (with T.Ibukiyama), This result has been generalized to some extent. Besides, we gave a remarkable result on the vanishing of the Maass zeta function.
6. Using the squared Moebius function, we gave a simpler proof to a result of T.Ibukiyama and H.Saito on an explicit form of the zeta function for symmetric matrices.
7. We gave a precise result on the demominator of a certain power series associated with local densities of quadratic forms.
|
