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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.29686 |
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| _version_ | 1866914435241607168 |
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| author | Choi, Seokhyun Im, Bo-Hae Kim, Beomho |
| author_facet | Choi, Seokhyun Im, Bo-Hae Kim, Beomho |
| contents | Let $E/k$ be a non-isotrivial elliptic curve over a global function field $k$ of characteristic $p>3$, and $G\subset \mathrm{Gal}(k^{\mathrm{sep}}/k)$ be a topologically finitely generated subgroup. We prove that if $E/k$ has analytic rank $1$, then its rank over the fixed subfield $L^G$ is infinite, where $L$ is the infinite ring class extension of some finite separable extension $K/k$. If $E/k$ has analytic rank $0$, then we prove that the same holds provided there exists an imaginary quadratic extension $K/k$ such that $E/K$ has analytic rank $1$ and satisfies the Heegner hypothesis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_29686 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Analytic rank-one elliptic curves over function fields and their rank over certain ring class fields Choi, Seokhyun Im, Bo-Hae Kim, Beomho Number Theory 11G05 Let $E/k$ be a non-isotrivial elliptic curve over a global function field $k$ of characteristic $p>3$, and $G\subset \mathrm{Gal}(k^{\mathrm{sep}}/k)$ be a topologically finitely generated subgroup. We prove that if $E/k$ has analytic rank $1$, then its rank over the fixed subfield $L^G$ is infinite, where $L$ is the infinite ring class extension of some finite separable extension $K/k$. If $E/k$ has analytic rank $0$, then we prove that the same holds provided there exists an imaginary quadratic extension $K/k$ such that $E/K$ has analytic rank $1$ and satisfies the Heegner hypothesis. |
| title | Analytic rank-one elliptic curves over function fields and their rank over certain ring class fields |
| topic | Number Theory 11G05 |
| url | https://arxiv.org/abs/2603.29686 |