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Theory of Hypergeometric Functions

Kazuhiko Aomoto, Michitake Kita (Autoren)

Buch | Hardcover

320 Seiten

2011
Springer Verlag, Japan
978-4-431-53912-4 (ISBN)

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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.

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.

Reihe/Serie	Springer Monographs in Mathematics
Mitarbeit	Anhang von: Toshitake Kohno
Übersetzer	Kenji Iohara
Zusatzinfo	XVI, 320 p.
Verlagsort	Tokyo
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
ISBN-10	4-431-53912-3 / 4431539123
ISBN-13	978-4-431-53912-4 / 9784431539124
Zustand	Neuware