On the order of magnitude of Sudler products II

Abstract

We study the asymptotic behavior of Sudler products PN(α)=∏Nr=12∣∣sinπrα∣∣ for quadratic irrationals α∈R. In particular, we verify the convergence of certain perturbed Sudler products along subsequences, and show that liminfNPN(α)=0 and limsupNPN(α)/N=∞ whenever the maximal digit in the period of the continued fraction expansion of α exceeds 23. This generalizes known results for the period one case α=[0;a¯¯¯].