On Kurzweil's 0-1 Law in Inhomogeneous Diophantine Approximation

Michael Fuchs, Dong Han Kim

We give a sufficient and necessary condition such that for almost all $s\in \mathbb{R}$ \[ \|nθ-s\|<ψ(n)\qquad\text{for infinitely many}\ n\in{\mathbb N}, \] where $\theta$ is fixed and…