Integral ratios of factorials and algebraic hypergeometric functions
Number Theory
2018-03-30 v1
Abstract
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.
Cite
@article{arxiv.math/0701362,
title = {Integral ratios of factorials and algebraic hypergeometric functions},
author = {Fernando Rodriguez Villegas},
journal= {arXiv preprint arXiv:math/0701362},
year = {2018}
}
Comments
Summary of talk at 2005 Explicit Methods in Number Theory, Oberwolfach