Aomoto / Kita Theory of Hypergeometric Functions

1. Auflage 2011
ISBN: 978-4-431-53938-4
Verlag: Springer Tokyo
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 320 Seiten

Reihe: Mathematics and Statistics

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.

Zielgruppe

Professional/practitioner

Autoren/Hrsg.

Aomoto, Kazuhiko

Kita, Michitake

Weitere Mitwirkende

Kohno, Toshitake

Iohara, Kenji

Inhaltsverzeichnis

1 Introduction: the Euler-Gauss Hypergeometric Function.- 2 Representation of Complex Integrals and Twisted de Rham Cohomologies.- 3 Hypergeometric functions over Grassmannians.- 4 Holonomic Difference Equations and Asymptotic Expansion References Index.