Convergence exponent of Pierce expansion digit sequences
Number Theory
2025-07-08 v3 Classical Analysis and ODEs
General Topology
Abstract
In this paper, we investigate the convergence exponent of Pierce expansion digit sequences. We explore some basic properties of the convergence exponent as a real-valued function defined on the closed unit interval, as well as those of the level sets of the function. Additionally, we further study subsets of the closed unit interval on which the series of positive th powers of the reciprocals of the Pierce expansion digits diverges.
Cite
@article{arxiv.2309.01722,
title = {Convergence exponent of Pierce expansion digit sequences},
author = {Min Woong Ahn},
journal= {arXiv preprint arXiv:2309.01722},
year = {2025}
}
Comments
28 pages, typos corrected