1998 Fiscal Year Final Research Report Summary
STUDIES ON D-MODULES DERIVED FROM CONFLUENT HYPERGEOMETRIC DIFFERENTIAL EQUATIONS
| Project/Area Number |
09440052
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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 |
解析学
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| Research Institution | Ochanomizu University |
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Principal Investigator |
MAJIMA Hideyuki Ochanomizu University Dept. Math. Prof., 理学部, 教授 (50111456)
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| Co-Investigator(Kenkyū-buntansha) |
IWASAKI Katsunori Kyushu University Dept. Math. Prof., 大学院・数理学研究科, 教授 (00176538)
ASAMOTO Nariko Ochanomizu University, Dept. Inf. Sci. Assoc. Prof., 理学部, 助教授 (90222603)
YOSHIDA Hiroaki Ochanomizu University, Dept. Inf. Sci. Assoc. Prof., 理学部, 助教授 (10220667)
TAKAYAMA Nobuki Kobe University Dept. MAth. Prof., 理学部, 教授 (30188099)
KIMURA Hironobu Kumamoto University Dept. Math. Prof., 理学部, 教授 (40161575)
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| Project Period (FY) |
1997 – 1998
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| Keywords | Confluent hypergeometric function / Irregukar singular / Irregularity / Asymptotic expansion / Period relation / Intersection theory / Divergent solution / Airy function |
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| Research Abstract |
1. Calculation of cohomology groups of solution complex of D-modules defined by confluent hypergeometric differential equations with values in the sheaves of germs of formal power-series ring and formal power-series ring with Gevrey order, by using projective resolutions of the D-modules similar to Koszul complex, which was invented by suggested information from 'KAN(a system' of computational algebraic analysis) made by Takayama
2. Asymptotic expansions of restrictions of generalized Airy functions by using relations between confluent hypergeometric functions with particular parameters and generalized Airy functions
3. Approximation formulas of coefficients of divergent solutions by using a vanishing theorem in asymptotic analysis in several variables
4. Constructionf of theory of intersection on the complex projective line for homology and cohomology groups defined by connections which are regular singular or not, and quadratic relations satisfied by confluent hypergeometric functions, as an analogue of period relations, by applying this theory.
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