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

Author: Pierre Le Boudec
Journal: Trans. Amer. Math. Soc. 372 (2019), 8347-8361
MSC (2010): Primary 11D45, 11G05, 11G50, 14G05
DOI: https://doi.org/10.1090/tran/7912
Published electronically: September 25, 2019
MathSciNet review: 4029699
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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 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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