Poor man's transcendence for Frobenius traces of elliptic curves

Fuente: arXiv
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Main Authors: Luca, Florian, Zudilin, Wadim
Format: Preprint
Published: 2025
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_version_ 1866911419116552192
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