Some exceptional sets of Borel-Bernstein theorem in continued fractions
Some exceptional sets of Borel-Bernstein theorem in continued fractions
复制标题
连分数中 Borel-Bernstein 定理的一些特殊集合
DOI：
10.1007/s11139-020-00320-8
复制
发表时间：
2021
影响因子：
0.7
通讯作者：
Song Kunkun
中科院分区：
文献类型：
--
作者：
Fang Lulu;Ma Jihua;Song Kunkun
Letdenote the continued fraction expansion of a real number. This paper is concerned with certain exceptional sets of the Borel–Bernstein Theorem on the growth rate of. As a main result, the Hausdorff dimension of the set \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} E_{\sup }(\psi )=\left\{ x\in [0,1):\ \limsup \limits _{n\rightarrow \infty }\frac{\log a_n(x)}{\psi (n)}=1\right\} \end{aligned}$$\end{document}is determined, wheretends to infinity as.
Letdenote the continued fraction expansion of a real number. This paper is concerned with certain exceptional sets of the Borel–Bernstein Theorem on the growth rate of. As a main result, the Hausdorff dimension of the set \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} E_{\sup }(\psi )=\left\{ x\in [0,1):\ \limsup \limits _{n\rightarrow \infty }\frac{\log a_n(x)}{\psi (n)}=1\right\} \end{aligned}$$\end{document}is determined, wheretends to infinity as.