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arXiv · 1912.00693

Location of small points on an elliptic curve by an equidistribution argument

Arnaud Plessis
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Abstract

Let $E$ be an elliptic curve defined over a number field $K$ without complex multiplication. If $Γ\subset E(\overline{K})$ is a subgroup of finite rank, a very special case of a conjecture of Rémond predicts that points of small height in $E(K(Γ))$ lie in the division group of $Γ$. Using an equidistribution argument, we will show that this conjecture is true for groups of rank arbitrarily large.

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Arnaud Plessis. 2023-03-28. Location of small points on an elliptic curve by an equidistribution argument. https://arxiv.org/abs/1912.00693

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