2014 Fiscal Year Final Research Report
Perrods and cogruences of modular forms
| Project/Area Number |
24540005
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Multi-year Fund |
|---|
| Section | 一般 |
|---|
| Research Field |
Algebra
|
|---|
| Research Institution | Muroran Institute of Technology |
|---|
Principal Investigator |
KATSURADA Hidenori 室蘭工業大学, 工学(系)研究科(研究院), 教授 (80133792)
|
|---|
| Project Period (FY) |
2012-04-01 – 2015-03-31
|
| Keywords | congruence / lift / L-values / Koecher-Maass series / Gross-Keating invariant / Siegel series |
|---|
| Outline of Final Research Achievements |
We proposed conjectures on prime ideals giving congruence between various lifts (eg. Ikeda-Miyawaki lift, Kim-Shahidi lift) and modular forms not coming from the lifts. I also gave numerical examples which support the conjectures. (Joint works with T. Ibukiyama, C. Poor, D. Yuen and S. Takemori) I gave an explicit formula for the twisted Koecher-Maass series of the Duke-Imamoglu-Ikeda lift.We also applied this to special values of the Rankin-Selberg series of half-integral weight modular form.
I investigated the properties of the Gross-Keating invariants of quadratic forms, and as an application we gave an explicit formula of the Siegel series of a quadartic forms over any non-archimedian local field.
|
| Free Research Field |
整数論
|
