Construction of normal bases by special values of modular functions
| Project/Area Number |
10640047
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Waseda University |
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Principal Investigator |
KOMATSU Keiichi Waseda University, School of Science and Engineering, Professor, 理工学部, 教授 (80092550)
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| 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)
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| Project Period (FY) |
1998 – 2000
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| Project Status |
Completed (Fiscal Year 2000)
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| Budget Amount *help |
¥1,600,000 (Direct Cost: ¥1,600,000)
Fiscal Year 2000: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 1999: ¥800,000 (Direct Cost: ¥800,000)
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| Keywords | Minkowski units / a ray class field / a Siegel modula function / a Jacobian variety / normal bases / Minkowski units / ray class field / 志村の相互法則 / 単数群 / ヤコーヒー多様体 / Greenberg予想 / Z_P-拡大 |
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| 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.
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Report
(4 results)
Research Products
(18 results)
