On Multiplicatively Badly Approximable Vectors

Reynold Fregoli, Dmitry Kleinbock

Let $⟨x⟩$ denote the distance from $x\in \mathbb{R}$ to the set of integers $\mathbb{Z}$. The Littlewood Conjecture states that for all pairs $(\hat{I}\pm ,{\hat{I}}^2)\in {\mathbb{R}}^2$…