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The Hausdorff dimension of certain sets in a class of α-Lüroth expansions

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Abstract

In this paper, we consider sets of points with some restricts on the digits of their α-Lüroth expansions. More precisely, for any countable partition α = {A n , n ∈ ℕ} of the unit interval I, we completely determine the Hausdorff dimensions of the sets

$$F\left( {\alpha ,\varphi } \right) = \left\{ {x = \left[ {l_1 \left( x \right),l_2 \left( x \right), \ldots } \right]_\alpha \in I:l_n \left( x \right) \geqslant \varphi \left( n \right),\forall _n \geqslant 1} \right\},$$

where φ is an arbitrary positive function defined on ℕ satisfying φ(n) → ∞ as n → ∞.

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Authors and Affiliations

  1. School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan, 430073, China

    HaiBo Chen

  2. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, 430074, China

    ZhiXiong Wen

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  1. HaiBo Chen
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  2. ZhiXiong Wen
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Correspondence to HaiBo Chen.

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Chen, H., Wen, Z. The Hausdorff dimension of certain sets in a class of α-Lüroth expansions. Sci. China Math. 57, 303–313 (2014). https://doi.org/10.1007/s11425-013-4606-0

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  • DOI: https://doi.org/10.1007/s11425-013-4606-0

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