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On the distribution of denominators in Sylvester expansions (II)
Published online by Cambridge University Press: 24 October 2003
Abstract
For any $x \in (0,1]$, let the series $ \sum_{n=1}^{\infty}1/d_n(x)$ be the Sylvester expansion of $x$. In this paper, we consider the Hausdorff dimension of the set $$B(\alpha, \beta)= \bigg\{x \in (0,1]: \lim\limits _{n \to \infty} \frac{d_{n+1}(x)}{d^{\beta}_n(x)}=\alpha\bigg\}$$ for any $\alpha \geq 0$ and $\beta \geq 2$. As a corollary, we answer the question posed by Goldie and Smith in [6].
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 135 , Issue 3 , November 2003 , pp. 421 - 430
- Copyright
- © 2003 Cambridge Philosophical Society
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