Integral ratios of factorials and algebraic hypergeometric functions

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.

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

Cited by in corpus (7)

• Ising n-fold integrals as diagonals of rational functions and integrality of series expansions
• An ansatz for the asymptotics of hypergeometric multisums
• Integral Factorial Ratios
• Bounded step functions and factorial ratio sequences
• $q$-rious and $q$-riouser
• Densities of bounded primes for hypergeometric series with rational parameters
• On integrality properties of hypergeometric series