A Lower Bound for the Canonical Height on Elliptic Curves over Abelian Extensions
نویسنده
چکیده
Let E/K be an elliptic curve defined over a number field, let ĥ be the canonical height on E, and let K/K be the maximal abelian extension of K. Extending work of Baker [4], we prove that there is a constant C(E/K) > 0 so that every nontorsion point P ∈ E(K) satisfies ĥ(P ) > C(E/K).
منابع مشابه
Lower Bounds for the Canonical Height on Elliptic Curves over Abelian Extensions
Let K be a number field and let E/K be an elliptic curve. If E has complex multiplication, we show that there is a positive lower bound for the canonical height of non-torsion points on E defined over the maximal abelian extension K of K. This is analogous to results of Amoroso-Dvornicich and Amoroso-Zannier for the multiplicative group. We also show that if E has non-integral j-invariant (so t...
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