| Project/Area Number |
16K05082
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Meijo University |
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Principal Investigator |
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| Project Period (FY) |
2016-04-01 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2018: ¥260,000 (Direct Cost: ¥200,000、Indirect Cost: ¥60,000)
Fiscal Year 2017: ¥390,000 (Direct Cost: ¥300,000、Indirect Cost: ¥90,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | Abelian function / sigma function / elliptic Gauss sums / Hecke L-series / algebraic curves / Jacobian varieties / sigma functions / heat equations / Abelian functions / algebraic curve / heat equation / Abel function / Hurwitz integrality / 代数曲線 / Coble suface / Jacobian variety |
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| Outline of Final Research Achievements |
(1) The researcher got the Hurwitz integrality of the power series expansion, at the origin, of the sigma function attached to a higher genus curve. The result is
published as a paper on Proceedings of Edinburgh Mathematical Society. (2) The researcher and coworkers, J.C. Eilbeck, J. Gibbons, and S. Yasuda, investigated the heat equations for multi-variate sigma functions and get explicit recursion formulae as well as precise formulation of the Buchstaber-Leykin theory on such heat equations. The result is submitted. (3) Investigated on elliptic Gauss sum expression of the Hecke L-values at 1, the researcher found the equivalence of vanishing and validity of Kummer-type congruence for the corresponding coefficients. The researcher gave several talk in the conferences, RIMS conference "Mathematical sturucture observed from theory of Integral systems and its applications", The 23rd Number theory conference at Waseda University", and twice of Aichi Numebr theory Seminar".
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| Academic Significance and Societal Importance of the Research Achievements |
本計画で得られた Abel 函数論の結果は, 伝統的な理論を深めるものであり, 楕円函数論がさうであつた様に, 数論に限らず, 様々な分野の数学で応用される様になるであらう.
また, 楕円 Gauss 和に関する結果は, additive reduction の場合の p-adic L-functions の研究に示唆を与へる可能性がある. さうでなくとも, Birch Swinnerton-Dyer 予想の意味することの広がりを実感するには, 身近な良い材料になると思ふ.
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