Quotient singularities, integer ratios of factorials and the Riemann Hypothesis

Abstract

The goal of this paper is to reveal a close connection between the following three subjects that have not been studied together in the past: terminal and canonical cyclic quotient singularities, integer ratios of factorials, Nyman's approach to the Riemann Hypothesis. In particular, we notice that the constructions of P.A. Picon are relevant for the study of singularities and possibly the Riemann Hypothesis. The list of the 29 stable quintuples of Mori-Morrison-Morrison coincides, up to the choice of notation, with the list of the 29 step functions with five terms of Vasyunin. We also reformulate and generalize a conjecture of Vasyunin.