标题： 关于函数域中的覆盖半径 显示英文标题

标题： On Covering Radii in Function Fields

摘要： 在本文中，我们将讨论正特征情况下数的几何中的主题，例如覆盖半径。 我们找到了相对于凸体的覆盖半径的闭合形式，这将导致在此设置下伍德斯猜想的正特征类似物的证明。 然后，我们将证明关于乘法覆盖半径的闵可夫斯基猜想的正特征类似物。 为此，我们将证明索兰结果的正特征类似物，即每个对角轨道都与良好圆化格子的集合相交。 这意味着在正特征情况下，格鲁伯-莫德尔谱在每个维度上都是平凡的。 显示英文摘要

摘要： In this paper, we shall discuss topics in geometry of numbers in the positive characteristic setting, such as covering radii. We find a closed form for covering radii with respect to convex bodies, which will lead to a proof of the positive characteristic analogue of Woods' conjecture in this setting. Then, we will prove a positive characteristic analogue of Minkowski's conjecture about the multiplicative covering radius. To do this, we shall prove a positive characteristic analogue of Solan's result that every diagonal orbit intersects the set of well rounded lattices. This implies that the Gruber-Mordell spectrum in positive characteristic is trivial in every dimension.