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Poor man's transcendence for Frobenius traces of elliptic curves

Florian Luca, Wadim Zudilin

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 adèle ring", we prove its transcendence over $\mathbb Q$.

Poor man's transcendence for Frobenius traces of elliptic curves

Abstract

Let be an elliptic curve without complex multiplication defined over . Viewing the sequence of its Frobenius traces indexed by primes as an element in the "poor man's adèle ring", we prove its transcendence over .

Paper Structure

This paper contains 2 theorems, 5 equations.

Key Result

Proposition 1

Let $\boldsymbol t=(t_p)_{p\in\mathcal{P}}\in\mathcal{A}$. The following conditions are equivalent.

Theorems & Definitions (3)

  • Proposition 1: Ro20
  • Theorem 1
  • proof