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.
| Author: Kazuhiko Aomoto |
| Publisher: Springer |
| Publication Date: May 13, 2011 |
| Number of Pages: 320 pages |
| Binding: Hardback or Cased Book |
| ISBN-10: 4431539123 |
| ISBN-13: 9784431539124 |
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