Diophantine approximation on manifolds and lower bounds for Hausdorff dimension

Victor Beresnevich, Lawrence Lee, Robert C. Vaughan +1

Given $n\in \mathbb{N}$ and $\tau >\frac{1}{n}$, let ${\mathcal{S}}_n(\tau )$ denote the classical set of $\tau$-approximable points in ${\mathbb{R}}^n$, which consists of $\mathbf{x}\in {\mathbb{R}}^n$ th…