On the order of magnitude of Sudler products II

2021/09/09 by Sigrid Grepstad, Grepstad, Sigrid, Mario Neumüller +3 · 1 citation
Mathematics · #11J70 #11J71 (Primary) #11L03 #26D05 (Secondary) #FOS: Mathematics #Mathematical Dynamics and Fractals #Meromorphic and Entire Functions #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2109.04342

openalex publication_date 2021/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the asymptotic behavior of Sudler products P_N(α)= ∏_r=1^N2|sin πrα| for quadratic irrationals α∈ ℝ. In particular, we verify the convergence of certain perturbed Sudler products along subsequences, and show that \liminf_N P_N(α) = 0 and \limsup_N P_N(α)/N = ∞ whenever the maximal digit in the continued fraction expansion of α exceeds 23. This generalizes results obtained for the period one case α=[0; a].

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