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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/2504.01965 |
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| _version_ | 1866912306510692352 |
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| author | Park, Jun-Yong Phillips, Tristan |
| author_facet | Park, Jun-Yong Phillips, Tristan |
| contents | As a consequence of their work on average Selmer ranks of elliptic curves with marked points, Bhargava and Ho proved that $100\%$ of elliptic curves over $\mathbb{Q}$ with an additional marked point have positive rank. In this note we provide an alternate proof which extends the result to global fields of characteristic not two or three. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_01965 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | 100% of elliptic curves with a marked point have positive rank Park, Jun-Yong Phillips, Tristan Number Theory 11G05, 11G50, 14D23 As a consequence of their work on average Selmer ranks of elliptic curves with marked points, Bhargava and Ho proved that $100\%$ of elliptic curves over $\mathbb{Q}$ with an additional marked point have positive rank. In this note we provide an alternate proof which extends the result to global fields of characteristic not two or three. |
| title | 100% of elliptic curves with a marked point have positive rank |
| topic | Number Theory 11G05, 11G50, 14D23 |
| url | https://arxiv.org/abs/2504.01965 |