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arXiv · 2308.03071

On Covering Radii in Function Fields

Noy Soffer Aranov
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Abstract

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.

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Noy Soffer Aranov. 2023-08-06. On Covering Radii in Function Fields. https://arxiv.org/abs/2308.03071

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