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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2502.17678 |
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| _version_ | 1866910843210301440 |
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| author | Burrin, Claire Gröbner, Matthias |
| author_facet | Burrin, Claire Gröbner, Matthias |
| contents | We consider rational points on the sphere and investigate their equidistribution in shrinking spherical caps. For the two-dimensional sphere, we leverage Hecke operators to obtain a significantly improved small-scale equidistribution bound, and discuss connections to the covering radius problem, intrinsic Diophantine approximation, and Linnik's conjecture on sums of two squares and a mini-square. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_17678 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Equidistribution, covering radius, and Diophantine approximation for rational points on the sphere Burrin, Claire Gröbner, Matthias Number Theory We consider rational points on the sphere and investigate their equidistribution in shrinking spherical caps. For the two-dimensional sphere, we leverage Hecke operators to obtain a significantly improved small-scale equidistribution bound, and discuss connections to the covering radius problem, intrinsic Diophantine approximation, and Linnik's conjecture on sums of two squares and a mini-square. |
| title | Equidistribution, covering radius, and Diophantine approximation for rational points on the sphere |
| topic | Number Theory |
| url | https://arxiv.org/abs/2502.17678 |