Study on hypergeometric functions
| Project/Area Number |
19340034
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Kyushu University |
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Principal Investigator |
YOSHIDA Masaaki Kyushu University, 大学院・数理学研究院, 教授 (30030787)
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| Co-Investigator(Kenkyū-buntansha) |
佐々木 武 神戸大学, 理学部, 教授 (00022682)
三町 勝久 東京工業大学, 理工学研究科, 教授 (40211594)
松本 圭司 北海道大学, 理学研究科, 准教授 (30229546)
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| Project Period (FY) |
2007 – 2010
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| Project Status |
Completed (Fiscal Year 2010)
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| Budget Amount *help |
¥7,540,000 (Direct Cost: ¥5,800,000、Indirect Cost: ¥1,740,000)
Fiscal Year 2010: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2009: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2008: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2007: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
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| Keywords | 黒写像 / 又黒写像 / 平前曲面 / 超幾何関数 / 絵有関数 / 離散曲面 / 平面配置 / 平行曲面族 / 焦曲面 / 離散平前曲面 / 超平面配置 / 舌寝配置 / 超幾何 / 交叉数 / 捻表路地群 / 平前 / 燕尾 / 特異点 / 絵有 / 離散 / 測多価群 / 共鳴 / 裏黒写像 / 白頭絡 |
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| Research Abstract |
We succeeded to find a good discretization of the hyperbolic Schwarz map for the Airy equation. This is the starting point of the study of singularities of discrete surfaces. For the hypergeometric differential equation of type (3,6), we found a relation between the two monodromy groups - arithmetic group acting of the domain of type IV, and the maximal non-real finite complex reflection group.
We described chambers cut out by six planes in general position in the 3-space.
Veronese arrangements of hyperplanes in real projective spaces re studied.
A set of generators of the monodromy group of the Appell-Lauricella's hypergeometric equation of type FA is obtained.
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Report
(6 results)
Research Products
(31 results)
