2000 Fiscal Year Final Research Report Summary
Construction of normal bases by special values of modular functions
| Project/Area Number |
10640047
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Algebra
|
|---|
| Research Institution | Waseda University |
|---|
Principal Investigator |
KOMATSU Keiichi Waseda University, School of Science and Engineering, Professor, 理工学部, 教授 (80092550)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
ADACHI Norio Wasede University, School of Science and Engineering, Professor, 理工学部, 教授 (60063731)
HASHIMOTO Kiichiro Waseda University, School of Science and Engineering, Professor, 理工学部, 教授 (90143370)
|
|---|
| Project Period (FY) |
1998 – 2000
|
| Keywords | Minkowski units / a ray class field / a Siegel modula function / a Jacobian variety / normal bases |
|---|
| Research Abstract |
In 1998, we have obtained the following ;
We constructed normal bases in the first layer of a Zp-extension of a certain abelian extension of (]SU.[) by special values of Siegel modular functions. We used the Jacobian variety with a principal polalization of the curve y^2=1-x^5.
In 1999, we have obtained the following ;
We constructed Minkowshi units in the ray class field of (]SU.[) modulo 6 by special velues of Siegel modular functions. We constructed also a unit group in the ray class field of (]SU.[) modulo 18 by special values of Siegel modular functions.
In 2000, we have obtained the following ;
We constructed all unies in the ray class field of (]SU.[) by special values of Siegel modular functions.
|
