GKZ systems with irregular singularities
| Project/Area Number |
13640172
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Basic analysis
|
|---|
| Research Institution | KOBE UNIVERSITY |
|---|
Principal Investigator |
TAKAYAMA Nobuki Kobe University Faculty of Science Professor, 理学部, 教授 (30188099)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
NORO Masayuki Kobe University Faculty of Science Professor, 理学部, 教授 (50332755)
|
|---|
| Project Period (FY) |
2001 – 2002
|
| Project Status |
Completed (Fiscal Year 2002)
|
| Budget Amount *help |
¥2,800,000 (Direct Cost: ¥2,800,000)
Fiscal Year 2002: ¥1,400,000 (Direct Cost: ¥1,400,000)
Fiscal Year 2001: ¥1,400,000 (Direct Cost: ¥1,400,000)
|
|---|
| Keywords | A-hypergeometric system / A-hypergeometric functions / irregular singularities / mathematical software / computer algebra / D-modules / numerical analysis / Kummer type identities / 自由分解 |
|---|
| 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.
|
Report
(3 results)
Research Products
(22 results)
