Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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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.

Discrete measures with dense jumps induced by Sturmian Dirichlet series

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