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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.17758 |
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| _version_ | 1866917722025099264 |
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| author | Chamizo, Fernando de la Hoz, Francisco |
| author_facet | Chamizo, Fernando de la Hoz, Francisco |
| contents | In this paper, we give a rigorous proof for the expression of the angle between adjacent sides in the skew polygons appearing at rational times in the evolution of regular polygons of $M$ sides under the vortex filament equation. The proof depends on showing that some exponential sums with arithmetic content are purely imaginary. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_17758 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Regular Polygonal Vortex Filament Evolution and Exponential Sums Chamizo, Fernando de la Hoz, Francisco Number Theory 35Q35, 35Q41, 11L03, 11R52 In this paper, we give a rigorous proof for the expression of the angle between adjacent sides in the skew polygons appearing at rational times in the evolution of regular polygons of $M$ sides under the vortex filament equation. The proof depends on showing that some exponential sums with arithmetic content are purely imaginary. |
| title | Regular Polygonal Vortex Filament Evolution and Exponential Sums |
| topic | Number Theory 35Q35, 35Q41, 11L03, 11R52 |
| url | https://arxiv.org/abs/2403.17758 |