基于等分布论证的椭圆曲线上小点位置
数论
2023-03-29 v5
摘要
设 为定义于数域 上无复乘法的椭圆曲线。若 为有限秩子群，Rémond猜想的一个非常特殊的情形预测 中小高度点落于 的除子群中。利用等分布论证，我们将证明该猜想对任意大秩的群均成立。
引用
@article{arxiv.1912.00693,
title = {Location of small points on an elliptic curve by an equidistribution argument},
author = {Arnaud Plessis},
journal= {arXiv preprint arXiv:1912.00693},
year = {2023}
}
备注
Amoroso pointed out that [14, Lemma 5.8] was false (a counterexample has been provided). Hence, the previous version has been modified in order to make it independent of this lemma. Consequently, the descent argument presented in Section 3 (and used in Section 4) is different. Moreover, the main theorem suffered a slight degradation. Final version