Chabauty Limits of Fermat Spirals
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908617415852032 |
|---|---|
| author | Tevet, Yohay Ailon |
| author_facet | Tevet, Yohay Ailon |
| contents | A Fermat spiral is a set of points of the form $\sqrt{n}e^{2πiαn}$ for $α\in \mathbb{R}$. In this paper we prove that the Chabauty limits of Fermat spirals are always closed subgroups of $\mathbb{R}^2$, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_22863 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Chabauty Limits of Fermat Spirals Tevet, Yohay Ailon Number Theory A Fermat spiral is a set of points of the form $\sqrt{n}e^{2πiαn}$ for $α\in \mathbb{R}$. In this paper we prove that the Chabauty limits of Fermat spirals are always closed subgroups of $\mathbb{R}^2$, 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. |
| title | Chabauty Limits of Fermat Spirals |
| topic | Number Theory |
| url | https://arxiv.org/abs/2506.22863 |