Chabauty Limits of Fermat Spirals

2025/06/28 by Tevet, Yohay Ailon
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2506.22863

Abstract

A Fermat spiral is a set of points of the form √(n)e^2πiαn for α∈ ℝ. In this paper we prove that the Chabauty limits of Fermat spirals are always closed subgroups of ℝ², and conclude that no Fermat spirals are dense forests. Furthermore, we show that if α is badly approximable the Chabauty limits are always lattices, for which we give a characterisation.

Citations

• Around the Danzer Problem and the Construction of Dense Forests
• Delone sets generated by square roots
• A better way to construct the sunflower head

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