Theory of hypergeometric functions
By: Kazuhiko Aomoto, Michitake Kita ; with an appendix by Toshitake Kohno
Contributors: Kita, Michitake, d. 1995; Kohno, Toshitake
Series: Springer monographs in mathematics; Springer monographs in mathematics
Publisher: Springer
Published: 2011
Place of publication: Tokyo; New York
Language: eng
Number of pages: 317
ISBN-13: 9784431539124; 9784431539384
Subjects: Hypergeometric functions
Work titles: Chōkika kansūron
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.
Notes: Includes bibliographical references (p. 307-314) and index.