A statistical view on the conjecture of Lang about the canonical height on elliptic curves

Le Boudec, Pierre

doi:10.1090/tran/7912

A statistical view on the conjecture of Lang about the canonical height on elliptic curves
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Trans. Amer. Math. Soc. 372 (2019), 8347-8361 Request permission

Abstract:

We adopt a statistical point of view on the conjecture of Lang which predicts a lower bound for the canonical height of nontorsion rational points on elliptic curves defined over $\mathbb {Q}$. More specifically, we prove that among the family of all elliptic curves defined over $\mathbb {Q}$ and having positive rank, there is a density one subfamily of curves which satisfy a strong form of Lang’s conjecture.

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