Scholarlink

<p>In this paper, we shall discuss topics in geometry of numbers in the function field 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 function field analogue of Woods’ conjecture in this setting. Then, we will prove a function field analogue of Minkowski’s conjecture about the multiplicative covering radius. To do this, we shall prove a function field analogue of Solan’s result that every diagonal orbit intersects the set of well rounded lattices. This implies that the Gruber–Mordell spectrum in function field is trivial in every dimension.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

On covering radii in function fields

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年1月9日

查看全文
  • Noy Soffer Aranov

摘要

In this paper, we shall discuss topics in geometry of numbers in the function field 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 function field analogue of Woods’ conjecture in this setting. Then, we will prove a function field analogue of Minkowski’s conjecture about the multiplicative covering radius. To do this, we shall prove a function field analogue of Solan’s result that every diagonal orbit intersects the set of well rounded lattices. This implies that the Gruber–Mordell spectrum in function field is trivial in every dimension.