Theory of Hypergeometric Functions
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ISBN-13:
9784431540878
Veröffentl:
2013
Einband:
Paperback
Erscheinungsdatum:
15.07.2013
Seiten:
336
Autor:
Kazuhiko Aomoto
Gewicht:
511 g
Format:
235x155x19 mm
Serie:
Springer Monographs in Mathematics
Sprache:
Englisch
Beschreibung:
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.
Reader will understand clearly multidimensional hypergeometric function as a natural extension of the classical one from viewpoint of integrals
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.
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