On the order of magnitude of Sudler products
2020
Given an irrational number $\alpha\in(0,1)$, the Sudler product is defined by $P_N(\alpha) = \prod_{r=1}^{N}2|\sin\pi r\alpha|$. Answering a question of Grepstad, Kaltenb\"ock and Neum\"uller we prove an asymptotic formula for distorted Sudler products when $\alpha$ is the golden ratio $(\sqrt{5}+1)/2$ and establish that in this case $\limsup_{N \to \infty} P_N(\alpha)/N 0$ and $\limsup_{N \to \infty} P_N(\alpha) / N < \infty$ hold, respectively. We establish that there is a (sharp) transition point at $a=6$, and resolve as a by-product a problem of the first named author, Larcher, Pillichshammer, Saad Eddin, and Tichy.
Keywords:
- Correction
- Source
- Cite
- Save
- Machine Reading By IdeaReader
26
References
6
Citations
NaN
KQI