A lower bound for the Hausdorff dimension of the set of weighted simultaneously approximable points over manifolds

Victor Beresnevich, Jason Levesley, Benjamin Ward

Given a weight vector $\tau =({\tau }_1,\dots ,{\tau }_n)\in {\mathbb{R}}_{+}^n$ with each ${\tau }_i$ bounded by certain constraints, we obtain a lower bound for the Hausdorff dimension of the…