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

By Jonathan W. Bober. 2007

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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 Vasyunin. Equivalently, we completely describe when certain sequences of ratios of factorial products are always integral. Essentially, once certain observations have been made, this comes down to an application of Beukers and Heckman's classification of the monodromy of the hypergeometric function nFn−1. We also note applications to the classification of cyclic quotient singularities.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/b266c444d10a1098aaca3eba79a6ae1e64032e39