2019
DOI: 10.1090/tran/7912
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A statistical view on the conjecture of Lang about the canonical height on elliptic curves

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 Q. More specifically, we prove that among the family of all elliptic curves defined over 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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