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Authors:	Jun Wu

Institution:	(1) Huazhong University of Science and Technology, Hubei, P.R. China

Abstract:	For ${\rm log}\frac{1+\sqrt{5}}{2}\leq \lambda_\ast \leq \lambda^\ast < \infty$ , let E(λ_, λ^) be the set $\left\{x\in 0,1):\ \mathop{\lim\inf}_{n \rightarrow \infty}\frac{\log q_n(x)}{n}=\lambda_{\ast}, \mathop{\lim\sup}_{n \rightarrow \infty}\frac{\log q_n(x)}{n}=\lambda^{\ast}\right\}.$ It has been proved in 1] and 3] that E(λ_, λ^) is an uncountable set. In the present paper, we strengthen this result by showing that $\dim E(\lambda_{\ast}, \lambda^{\ast}) \ge \frac{\lambda_{\ast} -\log \frac{1+\sqrt{5}}{2}}{2\lambda^{\ast}}$ where dim denotes the Hausdorff dimension.

Keywords:	2000 Mathematics Subject Classifications: 11K50 11J70 28A80
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