Abstract

Let $\beta>1$ be a real number. For any $x\in[0,1]$, let $r_{n}(x,\beta)$ be the maximal length of consecutive zero digits in the first $n$ digits of the $\beta$-expansion of $x$. In this note, it is proved that for any $0

DOI

10.3906/mat-1704-119

Keywords

$\beta$-Expansion, consecutive zero digits, Hausdorff dimension

First Page

656

Last Page

665

Recommended Citation

GAO, X, HU, H, & LI, Z (2018). A result on the maximal length of consecutive 0 digits in $\beta$-expansions. Turkish Journal of Mathematics 42 (2): 656-665. https://doi.org/10.3906/mat-1704-119

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