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arXiv · 2504.01965

100% of elliptic curves with a marked point have positive rank

Jun-Yong Park·Tristan Phillips
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Abstract

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.

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Jun-Yong Park, Tristan Phillips. 2025-03-18. 100% of elliptic curves with a marked point have positive rank. https://arxiv.org/abs/2504.01965

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