A zero-one Law for improvements to Dirichlet's Theorem

Dmitry Kleinbock, Nick Wadleigh

We give an integrability condition on a function $\psi$ guaranteeing that for almost all (or almost no) $x\in \mathbb{R}$, the system $|qx-p|\le \psi (t)$, $|q|<t$ is solvable in $p\in \m…