论文标题
晶格覆盖密度的新界限
New bounds on the density of lattice coverings
论文作者
论文摘要
我们通过扩张凸体K的扩张获得了欧几里得空间晶格覆盖率最小密度的新上限。我们还获得了概率（相对于晶格空间上的天然Haar-siegel测度）的界限，即随机选择的晶格l+满足L+k是所有空间。作为证明的一步，我们利用并加强了离散的Kakeya问题的结果。
We obtain new upper bounds on the minimal density of lattice coverings of Euclidean space by dilates of a convex body K. We also obtain bounds on the probability (with respect to the natural Haar-Siegel measure on the space of lattices) that a randomly chosen lattice L satisfies that L+K is all of space. As a step in the proof, we utilize and strengthen results on the discrete Kakeya problem.
