Hausdorff dimensions in Pierce expansions
Number Theory
2024-08-01 v2 Classical Analysis and ODEs
Abstract
The digits of Pierce expansion obey the law of large numbers, the central limit theorem, and the law of the iterated logarithm in the Lebesgue measure sense. We calculate the Hausdorff dimensions of the exceptional sets of each of the three laws. We further determine the Hausdorff dimensions of certain sets arising in Pierce expansions.
Keywords
Cite
@article{arxiv.2304.14162,
title = {Hausdorff dimensions in Pierce expansions},
author = {Min Woong Ahn},
journal= {arXiv preprint arXiv:2304.14162},
year = {2024}
}
Comments
46 pages; proof of Lemma 4.6 revised; typos corrected