On a Kurzweil type theorem via ubiquity
Number Theory
2024-01-30 v2
Abstract
Kurzweil's theorem ('55) is concerned with zero-one laws for well approximable targets in inhomogeneous Diophantine approximation under the badly approximable assumption. In this article, we prove the divergent part of a Kurzweil type theorem via a suitable construction of ubiquitous systems when the badly approximable assumption is relaxed. Moreover, we also discuss some counterparts of Kurzweil's theorem.
Cite
@article{arxiv.2306.00847,
title = {On a Kurzweil type theorem via ubiquity},
author = {Taehyeong Kim},
journal= {arXiv preprint arXiv:2306.00847},
year = {2024}
}
Comments
11 pages; Theorem 1.7 and its proof are revised