Xiang GAO, İ HU, Zhihui LI

A result on the maximal length of consecutive 0 digits in $\beta$-expansions

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

Keywords:

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

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ISSN: 1300-0098
Yayın Aralığı: 6
Yayıncı: TÜBİTAK

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