Theory of Hypergeometric Functions
Aomoto, Kazuhiko, Kita, Michitake
Produktnummer:
180aaba169906b49fe89f0c288f790c89b
| Autor: | Aomoto, Kazuhiko Kita, Michitake |
|---|---|
| Themengebiete: | Asymptotic behavior Holonomic system of difference equations Holonomic system of differential equations Hypergeomtric function Twisted de Rham cohomology |
| Veröffentlichungsdatum: | 13.05.2011 |
| EAN: | 9784431539124 |
| Sprache: | Englisch |
| Seitenzahl: | 320 |
| Produktart: | Gebunden |
| Verlag: | Springer Tokyo |
Produktinformationen "Theory of Hypergeometric Functions"
This book presents a geometric theory of complex analytic integrals representing hypergeometric functions of several variables. Starting from an integrand which is a product of powers of polynomials, integrals are explained, in an open affine space, as a pair of twisted de Rham cohomology and its dual over the coefficients of local system. It is shown that hypergeometric integrals generally satisfy a holonomic system of linear differential equations with respect to the coefficients of polynomials and also satisfy a holonomic system of linear difference equations with respect to the exponents. These are deduced from Grothendieck-Deligne’s rational de Rham cohomology on the one hand, and by multidimensional extension of Birkhoff’s classical theory on analytic difference equations on the other.
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