Integral ratios of factorials and algebraic hypergeometric functions

Details Integral ratios of factorials and algebraic hypergeometric functions Integral ratios of factorials and algebraic hypergeometric functions

2007-01-12

arxiv.org/abs/math/0701362v1

Mathematics

Number Theory

Summary of talk at 2005 Explicit Methods in Number Theory, Oberwolfach

Scientific paper

Sketch of proof of a theorem relating the two subjects of the title. It can be thought as an extension of results of Landau for the classical hypergeometric function. It relies on the characterization of algebraic hypergeometric functions of Beukers and Heckman. In the process we also show that a variant of a classical construction of Bezout (producing a quadratic form, the Bezoutian, out of two polynomials in one variable) gives the Hermitian form fixed by the monodromy group, up to scaling.

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