Representations of rational numbers and Minkowski dimension
Classical Analysis and ODEs
2025-12-25 v2 Number Theory
Abstract
In this paper, we investigate the representations of rational numbers via continued fraction, Egyptian fraction, and Engel fraction expansions. Given , denote by the sets of rational numbers whose continued fraction, Egyptian fraction, and Engel fraction expansions have length , respectively. We first establish the Minkowski dimensions of these sets, which implies that their global scaling properties are different. We also apply the results to sumsets of decreasing sequences.
Keywords
Cite
@article{arxiv.2510.17112,
title = {Representations of rational numbers and Minkowski dimension},
author = {Haipeng Chen and Lai Jiang and Yufeng Wu},
journal= {arXiv preprint arXiv:2510.17112},
year = {2025}
}