Theory of Hypergeometric Functions

Released on by Kazuhiko Aomoto
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  • Theory of Hypergeometric Functions Book Detail

  • Author : Kazuhiko Aomoto
  • Release Date : 2011-05-21
  • Publisher : Springer Science & Business Media
  • Genre : Mathematics
  • Pages : 327
  • ISBN 13 : 4431539387
  • File Size : 54,54 MB
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Theory of Hypergeometric Functions by Kazuhiko Aomoto PDF Summary

Book Description: 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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