Bull. Korean Math. Soc. 2015; 52(6): 1797-1803
Printed November 30, 2015
https://doi.org/10.4134/BKMS.2015.52.6.1797
Copyright © The Korean Mathematical Society.
DoYong Kwon
Chonnam National University
Let $(s_\alpha(n))_{n\geq1}$ be the lexicographically greatest Sturmian word of slope $\alpha>0$. For a fixed $\sigma>1$, we consider Dirichlet series of the form $\nu_\sigma(\alpha):=\sum_{n=1}^\infty s_\alpha(n) n^{-\sigma}$. This paper studies the singular properties of the real function $\nu_\sigma$, and the Lebesgue-Stieltjes measure whose distribution is given by $\nu_\sigma$.
Keywords: Dirichlet series, singular function, Sturmian word
MSC numbers: 11M41, 26A30, 68R15
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