Theory of Hypergeometric Functions

2011
ISBN: 978-4-431-54087-8
Verlag: Springer Japan

Buch, Englisch, 320 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 511 g

Reihe: Springer Monographs in Mathematics

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

Iohara, Kenji

Kohno, Toshitake

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Differentialgeometrie
• Mathematik | Informatik Mathematik Topologie Algebraische Topologie
• Mathematik | Informatik Mathematik Mathematische Analysis Integralrechnungen- und -gleichungen

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.