Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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DISCRETE MEASURES WITH DENSE JUMPS INDUCED BY STURMIAN DIRICHLET SERIES

  • KWON, DOYONG (Department of Mathematics Chonnam National University)
  • Received : 2014.02.06
  • Published : 2015.11.30
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Abstract

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 ${\nu}_{\sigma}$.

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References

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