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arXiv · 2507.14773

Poor man's transcendence for Frobenius traces of elliptic curves

Florian Luca·Wadim Zudilin
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Abstract

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 ad\`ele ring", we prove its transcendence over $\mathbb Q$.

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Florian Luca, Wadim Zudilin. 2025-07-20. Poor man's transcendence for Frobenius traces of elliptic curves. https://arxiv.org/abs/2507.14773

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