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.
| Autorius: | Kazuhiko Aomoto, Michitake Kita, |
| Serija: | Springer Monographs in Mathematics |
| Leidėjas: | Springer Japan |
| Išleidimo metai: | 2013 |
| Knygos puslapių skaičius: | 336 |
| ISBN-10: | 4431540873 |
| ISBN-13: | 9784431540878 |
| Formatas: | 235 x 155 x 19 mm. Knyga minkštu viršeliu |
| Kalba: | Anglų |
Parašykite atsiliepimą apie „Theory of Hypergeometric Functions“
