On the order of magnitude of Sudler products II
Sigrid Grepstad, Mario Neumüller, Agamemnon Zafeiropoulos · International Journal of Number Theory · 2022
We study the asymptotic behavior of Sudler products [Formula: see text] for quadratic irrationals [Formula: see text]. In particular, we verify the convergence of certain perturbed Sudler products along subsequences, and show that [Formula: see text] and [Formula: see text] whenever the maximal digit in the period of the continued fraction expansion of [Formula: see text] exceeds [Formula: see text]. This generalizes known results for the period one case [Formula: see text].