Theory of Hypergeometric Functions

  • Kazuhiko Aomoto
  • Michitake Kita

Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Kazuhiko Aomoto, Michitake Kita
    Pages 1-19
  3. Kazuhiko Aomoto, Michitake Kita
    Pages 21-101
  4. Kazuhiko Aomoto, Michitake Kita
    Pages 183-259
  5. Back Matter
    Pages 261-317

About this book

Introduction

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.

Keywords

Asymptotic behavior Holonomic system of difference equations Holonomic system of differential equations Hypergeomtric function Twisted de Rham cohomology

Authors and affiliations

  • Kazuhiko Aomoto
    • 1
  • Michitake Kita
  1. 1.Nagoya UniversityNagoyaJapan

Bibliographic information

  • DOI https://doi.org/10.1007/978-4-431-53938-4
  • Copyright Information Springer 2011
  • Publisher Name Springer, Tokyo
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-4-431-53912-4
  • Online ISBN 978-4-431-53938-4
  • Series Print ISSN 1439-7382
  • About this book
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