On a Kurzweil type theorem via ubiquity
Acta Arithmetica
MSC: Primary 11J20; Secondary 11J83, 28A78
DOI: 10.4064/aa230609-27-1
Published online: 4 April 2024
Abstract
Kurzweil’s theorem (1955) 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.
