2006 Fiscal Year Final Research Report Summary
Special values of Siegel modular functions and Jacobian variety
| Project/Area Number |
16540046
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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, Faculty of Science and Engineering, Professor, 理工学術院, 教授 (80092550)
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| Co-Investigator(Kenkyū-buntansha) |
HASHIMOTO Kiichiro Waseda University, Faculty of Science and Engineering, Professor, 理工学術院, 教授 (90143370)
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| Project Period (FY) |
2004 – 2006
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| Keywords | ray class field / unit / abelian variety / λ-invariant |
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| Research Abstract |
We construct certain algebraic integers αm as special values of two variable theta functions in the ray class field of a certain quartic field modulo 2m, and study a property of prime i deals which appear in αm in connection to the relationships between cyclotomic units and exponential functions and between elliptic units and elliptic functions, Moreover, we study a relationship between the Mordell-Weil rank of an abelian variety with complex multiplication and the Iwasawa λ-invariant of a certain ZLP-extension.
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