Metric Discrepancy Results for Subsequences of Geometric Progressions
Metric Discrepancy Results for Subsequences of Geometric Progressions
复制标题
几何级数子序列的公制差异结果
DOI：
10.1134/s1995080222010085
复制
发表时间：
2021
影响因子：
0.7
通讯作者：
Suzaki K.
中科院分区：
文献类型：
--
作者：
Fukuyama K.;Suzaki K.
In the previous work, we proved the law of the iterated logarithm for a subsequence of geometric progression \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\{\theta^{k}x\}$$\end{document} and showed that the speed of convergence toward the uniform distribution is faster than that of the original sequence. It is natural to ask if the speed becomes faster again if we take a subsequence of the subsequence. In this note, we give a negative answer to this question by giving a counterexample.
In the previous work, we proved the law of the iterated logarithm for a subsequence of geometric progression \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\{\theta^{k}x\}$$\end{document} and showed that the speed of convergence toward the uniform distribution is faster than that of the original sequence. It is natural to ask if the speed becomes faster again if we take a subsequence of the subsequence. In this note, we give a negative answer to this question by giving a counterexample.