A singular function from Sturmian continued fractions
J. Korean Math. Soc. 2019 Vol. 56, No. 4, 1049-1061
Published online July 1, 2019
DoYong Kwon
Chonnam National University
Abstract : For $\alpha\geq1$, let $s_\alpha(n)=\lceil\alpha n \rceil - \lceil \alpha (n-1) \rceil$. A continued fraction $C(\alpha)=[0; s_\alpha(1), s_\alpha(2),\ldots]$ is considered and analyzed. Appealing to Diophantine approximation, we investigate the differentiability of $C(\alpha)$, and then show its singularity.
Keywords : singular function, continued fraction, Diophantine approximation, Sturmian word
MSC numbers : 26A30, 11A55, 11J04, 68R15
Supported by : This research was supported by Basic Science Research Program through the National Resear ch Foundation of Korea (NRF) funded by the Ministry of Education (grant number: NRF-2016R1D1A1B020 10219).
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