Abstract
In the previous work, we proved the law of the iterated logarithm for a subsequence of geometric progression \(\{\theta^{k}x\}\) 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.
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(Submitted by A. I. Volodin)
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Fukuyama, K., Suzaki, K. Metric Discrepancy Results for Subsequences of Geometric Progressions. Lobachevskii J Math 42, 3123–3126 (2021). https://doi.org/10.1134/S1995080222010085
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DOI: https://doi.org/10.1134/S1995080222010085