On the order of magnitude of Sudler products II
Peer reviewed, Journal article
Accepted version
Permanent lenke
https://hdl.handle.net/11250/3052057Utgivelsesdato
2022Metadata
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- Institutt for matematiske fag [2360]
- Publikasjoner fra CRIStin - NTNU [37325]
Sammendrag
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¯¯¯].