1998 Fiscal Year Final Research Report Summary
Invariants of 3-manifolds and Dedekind sums
| Project/Area Number |
09640131
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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, Faculty of Liberal Arts, Professor, 学芸学部, 教授 (20011687)
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| Co-Investigator(Kenkyū-buntansha) |
SAKAMOTO Koichi Tsuda College, Faculty of Liberal Arts, Professor, 学芸学部, 教授 (40090518)
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| Project Period (FY) |
1997 – 1998
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| Keywords | manifold / topological invariant / low dimensional manifold / Dedekind sums / modular form / Jacobi form |
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| Research Abstract |
The head investigator have studied the relationship between generalized Dedekind sums and modular forms. These are closely related to topological invariants of manifolds. In his paper titled "Modular forms, generalized Dedekind symbols and period polynomials", the investigator clarified the relationship between these three objects.
He also applied the theory to the typical modular form -- the Eisenstein series. In his paper "Generalized Dedekind symbols associated with the Elsenstein series", he proved that Dedekind symbol associated with Bisenstein series is Apostol' s sums in essence. The paper will be published soon.
He published the paper tided "The space of period polynomials" which shows that period polynomials are expressed in terms of Bernoulli polynomials. This seems very interesting.
Recently he is trying to define Dedekind symbols to broader class of forms and made two preprint : "Dedekind symbols associated with Jacobi forms and their reciprocity law" and "twisted generalized Dedekind symbols"
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