DISCRETE MEASURES WITH DENSE JUMPS INDUCED BY STURMIAN DIRICHLET SERIES

Let ($S_{\alpha}(n))_{n{\geq}1}$ be the lexicographically greatest Sturmian word of slope ${\alpha}$ > 0. For a fixed ${\sigma}$ > 1, we consider Dirichlet series of the form ${\nu}_{\sigma}({\alpha})$ := ${\Sigma}_{n=1}^{\infty}s_{\alpha}(n)n^{-{\sigma}}$. This paper studies the singular properties of the real function ${\nu}_{\sigma}$, and the Lebesgue-Stieltjes measure whose distribution is given by ${\nu}_{\sigma}$.