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Theory of Hypergeometric Functions by Kazuhiko Aomoto

Theory of Hypergeometric Functions

by Kazuhiko Aomoto
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Book cover type: Paperback
  • ISBN13: 9784431540878
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Springer
  • Publisher Imprint: Springer
  • Publication Date:
  • Pages: 320
  • Original Price: EUR 89.99
  • Language: English
  • Edition: 2011
  • Item Weight: 481 grams
  • BISAC Subject(s): Geometry / General, Functional Analysis, and Calculus

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.

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