Discrete measures with dense jumps induced by Sturmian Dirichlet series
Bull. Korean Math. Soc. 2015 Vol. 52, No. 6, 1797-1803
Published online November 30, 2015
DoYong Kwon
Chonnam National University
Abstract : 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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