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arXiv · 1902.08435

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

Pierre Le Boudec
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Abstract

We adopt a statistical point of view on the conjecture of Lang which predicts a lower bound for the canonical height of non-torsion 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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Pierre Le Boudec. 2019-02-22. A statistical view on the conjecture of Lang about the canonical height on elliptic curves. https://arxiv.org/abs/1902.08435

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