2002 Fiscal Year Final Research Report Summary
GKZ systems with irregular singularities
| Project/Area Number |
13640172
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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 |
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)
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| Project Period (FY) |
2001 – 2002
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| Keywords | A-hypergeometric system / A-hypergeometric functions / irregular singularities / mathematical software / computer algebra / D-modules / numerical analysis / Kummer type identities |
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| Research Abstract |
We have obtained the following results.
(1) The hypergeometric system E_<k, n> is defined on the Grassmanian variety and it has a lot of nice properties. We gave an algorithmic method to derive Kummer type formulas for solutions of the system E_<k, n>. (2) We gave a new method for numerical evaluation of hypergeometric functions in several variables including GKZ hypergeometric functions. Our method translates a given hypergeometric equations into a systems of linear partial differential equations for which standard techniques of numerical analysis can be easily applied. This translation is done by using the Grobner basis method. (3) Slope is a fundamental invariant at irregular singular points. We determined the slopes for GKZ systems associated to monomial curves.
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