Hausdorff Dimension of Weighted Singular Vectors

Bohan Yang, Tianru Zhu

Let $d\ge 2$ and let $\mathbf{w}=(w_1,\dots ,w_d)$ satisfy $w_1\ge \cdots \ge w_d>0$ and ${\sum }_i{w}_i=1$. Set $s_{\ast }=d-(1+w_1{)}^{-1}$. We prove that there exist constants $C_{d,\mathbf w}>…