Factorial ratios, hypergeometric series, and a family of step functions

Details Factorial ratios, hypergeometric series, and a family of step functions Factorial ratios, hypergeometric series, and a family of step functions

2007-09-13

arxiv.org/abs/0709.1977v1

Mathematics

Number Theory

23 pages, 2 tables

Scientific paper

We give a complete classification of a certain family of step functions related to the Nyman--Beurling approach to the Riemann hypothesis and previously studied by V. I. Vasyunin. Equivalently, we completely describe when certain sequences of ratios of factorial products are always integral. Essentially, once certain observations are made, this comes down to an application of Beukers and Heckman's classification of the monodromy of the hypergeometric function nF_{n-1}. We also note applications to the classification of cyclic quotient singularities.

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