2005 Fiscal Year Final Research Report Summary
General study of modular forms and arithmetic varieties
| Project/Area Number |
16540042
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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 | Tokyo University of Science |
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Principal Investigator |
HAMAHATA Yoshinori Tokyo University of Science, Faculty of Science and Engineering, Associate Professor, 理工学部, 助教授 (90260645)
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| Co-Investigator(Kenkyū-buntansha) |
AGOH Takashi Tokyo University of Science, Faculty of Science and Engineering, Professor, 理工学部, 教授 (60112893)
HOSOH Toshio Tokyo University of Science, Faculty of Science and Engineering, Associate Professor, 理工学部, 助教授 (30130339)
AOKI Hiroki Tokyo University of Science, Faculty of Science and Engineering, Lecturer, 理工学部, 講師 (10333189)
GOTO Takeshi Tokyo University of Science, Faculty of Science and Engineering, Research Associate, 理工学部, 助手 (20366438)
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| Project Period (FY) |
2004 – 2005
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| Keywords | modular forms / elliptic curves |
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| Research Abstract |
The purpose of head investigator was to study properties of Hilbert modular cusps. We joined some workshops and seminars to get information and discuss about modular forms. We organized a workshop on Hilbert modular forms. Thanks to this workshop, we understood fundamental and recent results.
Our results are as follows :
1.We established some results on the structure of rings of modular forms and infinite products of modular forms.
2.We established some results on the existence of perfect numbers and their analogue.
3.We described Selmer groups of elliptic curves in terms of graphs.
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