Theory of hypergeometric functions
Kazuhiko Aomoto · 2011
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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.
Book details
- Year
- 2011
- Language
- English
- Series
- Springer monographs in mathematics
- Publisher
- Springer
- Editions
- 2
- Pages
- 317
- ISBN
- 9784431539124
Data source: Wikidata