2013 Fiscal Year Final Research Report
Knot invariants, modular forms and elliptic Dedekind sums
| Project/Area Number |
22540096
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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 |
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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) |
2010-04-01 – 2014-03-31
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| Keywords | 位相幾何学 / 保型形式 / デデキント和 |
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| Research Abstract |
The feature of our work is that we study Dedekind symbols in the relation with modular forms. Thus it is a significant step that we have constructed nice bases for the vector spaces of modular forms. We also obtained formulas to express powers of the theta function in terms of Eisenstein series. These formulas give us formulas for the numbers of representations of integers as sums of squares. These seem interesting from number theoretical and geometrical view points.
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