Poor man's transcendence for Frobenius traces of elliptic curves

Published 20 Jul 2025 in math.NT | (2507.14773v1)

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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