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- W4287725507 abstract "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 set of $tau$-approximable points points over a manifold $mathcal{M}$, where $mathcal{M}$ is twice continuously differentiable. From this we produce a lower bound for the set of $psi$-approximable points over a manifold where $psi$ is a general approximation function with certain limits. The proof is based on a technique developed by Beresnevich et al. in arXiv:1712.03761, but we use an alternative mass transference style theorem." @default.
- W4287725507 created "2022-07-26" @default.
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- W4287725507 date "2020-07-09" @default.
- W4287725507 modified "2023-09-24" @default.
- W4287725507 title "A lower bound for the Hausdorff dimension of the set of weighted simultaneously approximable points over manifolds" @default.
- W4287725507 doi "https://doi.org/10.48550/arxiv.2007.04742" @default.
- W4287725507 hasPublicationYear "2020" @default.
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