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

Research output: Contribution to journalArticle (Academic Journal)peer-review

34 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)422-444
Number of pages23
JournalJournal of the London Mathematical Society
Issue number2
Early online date13 Feb 2009
Publication statusPublished - Apr 2009

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