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On a Kurzweil type theorem via ubiquity

Volume 213 / 2024

Taehyeong Kim Acta Arithmetica 213 (2024), 181-191 MSC: Primary 11J20; Secondary 11J83, 28A78 DOI: 10.4064/aa230609-27-1 Published online: 4 April 2024


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.


  • Taehyeong KimThe Einstein Institute of Mathematics
    The Hebrew University of Jerusalem
    Jerusalem, 91904, Israel

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