2012 Fiscal Year Final Research Report
Geometric study of special functions
| Project/Area Number |
22540038
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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 | Hokkaido University |
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Principal Investigator |
MATSUMOTO Keiji 北海道大学, 大学院・理学研究院, 教授 (30229546)
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| Co-Investigator(Renkei-kenkyūsha) |
TERASOMA Tomohide 東京大学, 大学院・数理科学研究科, 教授 (50192654)
SHIGA Hironori 千葉大学, 大学院・理学研究科, 名誉教授 (90009605)
YOSHIDA Masaaki 九州大学, 大学院・数理学研究院, 教授 (30030787)
OHARA Katsuyoshi 金沢大学, 数物科学系, 准教授 (00313635)
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| Project Period (FY) |
2010 – 2012
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| Keywords | 超幾何関数 / テータ関数 / 算術幾何平均 / 局所系係数(コ)ホモロジー群 |
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| Research Abstract |
We construct several formulas for hypergeometric functions and systems of differential equations of multi-variables. (1) By using the intersection forms defined between twisted (co)homology groups, we give monodromy representations and connection matrices of Pfaffians for some of them. (2) For hypergeometric functions with special parameters related to periods of algebraic varieties, we give some identities between automorphic forms and hypergeometric functions. (3) Some limits defined by the iteration of several means of several terms are expressed by hypergeometric functions of multi-variables.
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