A dichotomy phenomenon for Bad minus normed Dirichlet

Dmitry Kleinbock, Anurag Rao

Given a norm $\nu$ on ${\mathbb{R}}^2$, the set of $\nu$-Dirichlet improvable numbers ${\mathbf{DI}}_{\nu }$ was defined and studied in the papers of Andersen-Duke (Acta Arith. 2021) and Kleinb…