2009 Fiscal Year Final Research Report
Study on Hecke operators for cusp forms and topological invariants
| Project/Area Number |
19540101
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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 |
Geometry
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| Research Institution | Tsuda College |
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Principal Investigator |
FUKUHARA Shinji Tsuda College, 学芸学部, 教授 (20011687)
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| Co-Investigator(Kenkyū-buntansha) |
MIYAZAWA Haruko 津田塾大学, 計数研, 研究員 (40266276)
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| Project Period (FY) |
2007 – 2009
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| Keywords | 位相幾何 |
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| Research Abstract |
Cusp forms on the complex upper half plane have been studied for the connection with number theory. The feature of our research is focusing on natural correspondences between cusp forms, periods and Dedekind symbols. We have introduced the notion of elliptic Apostol-Dedekind sums and showed these sums generate Dedekind symbols with polynomial reciprocity laws. We also studied how we can apply these sums to knot theory.
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