ENGLISH

Theory of hypergeometric functions

By Kazuhiko Aomoto , Michitake Kita (auth.)

Book information

Publisher
Springer Tokyo
Year
2011
ISBN
4431539123, 9784431539124
DOI
10.1007/978-4-431-53938-4
Open Library ID
OL25214264M
Language
english
Format
PDF
Filesize
2 MB (2099236 bytes)
Series
Springer Monographs in Mathematics
Edition
1
Pages
320\335
Library
Kolxo3
Time added
2011-07-22 07:35:22
Geometry; Functional Analysis

Description

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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