论文标题
同时在歧管上同时近似值点的Hausdorff尺寸的下限
A lower bound for the Hausdorff dimension of the set of weighted simultaneously approximable points over manifolds
论文作者
论文摘要
给定重量矢量$τ=（τ_{1}，\ dots，τ_{n}）\ in \ Mathbb {r}^{n} _ {n} _ {+} $，每个$τ_{i} $受某些约束所包围的，我们为Hausdorff $ nowers of Hausdorff $ set $ - aff set $ - aff set $ - $ \ MATHCAL {M} $，其中$ \ Mathcal {M} $连续两次可区分。由此，我们在$ψ$ appro-approable点的集合中产生了一个下限，其中$ψ$是具有一定限制的一般近似函数。证明是基于Beresnevich等人开发的技术。在Arxiv：1712.03761中，但我们使用另一种质量转移样式定理。
Given a weight vector $τ=(τ_{1}, \dots, τ_{n}) \in \mathbb{R}^{n}_{+}$ with each $τ_{i}$ bounded by certain constraints, we obtain a lower bound for the Hausdorff dimension of the set of $τ$-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 $ψ$-approximable points over a manifold where $ψ$ 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.
