| Project/Area Number |
15340045
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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 | KOBE UNIVERSITY |
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Principal Investigator |
TAKAYAMA Nobuki Kobe University, Faculty of Science, Professor, 理学部, 教授 (30188099)
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| Co-Investigator(Kenkyū-buntansha) |
NORO Masayuki Kobe University, Faculty of Science, Professor, 理学部, 教授 (50332755)
FUKUYAMA Katsushi Kobe University, Faculty of Science, Professor, 理学部, 教授 (60218956)
MASUDA Tetsu Kyoto University, Graduate School of Science, COE Researche, 理学研究科, COE研究員 (00335457)
OAKU Toshinori Tokyo Women's Christian University, Faculty of Literature and Science, Professor, 文理学部, 教授 (60152039)
SAITO Mutsumi Hokaido University, Graduate School of Science, Associate Profsor, 理学研究科, 助教授 (70215565)
松本 圭司 北海道大学, 理学研究科, 助教授 (30229546)
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| Project Period (FY) |
2003 – 2006
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| Project Status |
Completed (Fiscal Year 2006)
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| Budget Amount *help |
¥10,200,000 (Direct Cost: ¥10,200,000)
Fiscal Year 2006: ¥2,200,000 (Direct Cost: ¥2,200,000)
Fiscal Year 2005: ¥3,400,000 (Direct Cost: ¥3,400,000)
Fiscal Year 2004: ¥2,300,000 (Direct Cost: ¥2,300,000)
Fiscal Year 2003: ¥2,300,000 (Direct Cost: ¥2,300,000)
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| Keywords | A-hypergeometric function / A-hypergeometric equation / D-modules / Computational D-modules / Grobner basis / Mathematical formula / Special function / random numbers and integration / calA-超幾何関数 / calA-超幾何方程式 / 超幾何関数の積分表示 |
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| Research Abstract |
We have obtained the following results
1. We constructed vol(A)-linearly independent convergent series solutions for A-hypergeometric differential-difference equations.
2. We prove that any local Grober fan is a polyhedral fan. As an application of this fact, we give an algorithm of computing local BS polynomials, that of computing local tropical varieties, and discuss a relation of slopes and local Grobner fan.
3. We gave a tangent cone algorithm to study D-modules locally.
We have more results. As to these, refer to Japanese version of this research report and papers.
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