Poor man's transcendence for Frobenius traces of elliptic curves
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911419116552192 |
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| author | Luca, Florian Zudilin, Wadim |
| author_facet | Luca, Florian Zudilin, Wadim |
| contents | Let $E$ be an elliptic curve without complex multiplication defined over $\mathbb Q$. Viewing the sequence of its Frobenius traces $(a_p(E))_p$ indexed by primes $p$ as an element in the "poor man's adèle ring", we prove its transcendence over $\mathbb Q$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_14773 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Poor man's transcendence for Frobenius traces of elliptic curves Luca, Florian Zudilin, Wadim Number Theory 11J81 (primary), 11A41, 11J72, 11B83, 11G05, 11G07, 13A35, 16U10 (secondary) Let $E$ be an elliptic curve without complex multiplication defined over $\mathbb Q$. Viewing the sequence of its Frobenius traces $(a_p(E))_p$ indexed by primes $p$ as an element in the "poor man's adèle ring", we prove its transcendence over $\mathbb Q$. |
| title | Poor man's transcendence for Frobenius traces of elliptic curves |
| topic | Number Theory 11J81 (primary), 11A41, 11J72, 11B83, 11G05, 11G07, 13A35, 16U10 (secondary) |
| url | https://arxiv.org/abs/2507.14773 |