函数域上椭圆曲线典型高度的雷默型下界

IF 0.6 3区数学 Q3 MATHEMATICS

Journal of Number Theory Pub Date : 2024-05-16 DOI:10.1016/j.jnt.2024.04.004

Joseph H. Silverman

引用次数: 0

摘要

设 F 是代数闭域上的曲线的函数域，char(F)≠2,3，并设 E/F 是非等离椭圆曲线。那么，对于所有有限扩展 K/F 和所有非扭转点 P∈E(K)，P 的 F 归一化正则高度在下面有界：hˆE(P)≥110500⋅hF(jE)2⋅[K:F]2。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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A Lehmer-type lower bound for the canonical height on elliptic curves over function fields

Let $F$ be the function field of a curve over an algebraically closed field with $char (F) \neq 2, 3$ , and let $E / F$ be a non-isotrivial elliptic curve. Then for all finite extensions $K / F$ and all non-torsion points $P \in E (K)$ , the $F$ -normalized canonical height of P is bounded below by ${\hat{h}}_{E} (P) \geq \frac{1}{10500 \cdot h_{F} {(j_{E})}^{2} \cdot {[K : F]}^{2}} .$

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来源期刊

Journal of Number Theory 数学-数学

CiteScore

1.30

自引率

14.30%

发文量

122

审稿时长

16 weeks

期刊介绍： The Journal of Number Theory (JNT) features selected research articles that represent the broad spectrum of interest in contemporary number theory and allied areas. A valuable resource for mathematicians, the journal provides an international forum for the publication of original research in this field. The Journal of Number Theory is encouraging submissions of quality, long articles where most or all of the technical details are included. The journal now considers and welcomes also papers in Computational Number Theory. Starting in May 2019, JNT will have a new format with 3 sections: JNT Prime targets (possibly very long with complete proofs) high impact papers. Articles published in this section will be granted 1 year promotional open access. JNT General Section is for shorter papers. We particularly encourage submission from junior researchers. Every attempt will be made to expedite the review process for such submissions. Computational JNT . This section aims to provide a forum to disseminate contributions which make significant use of computer calculations to derive novel number theoretic results. There will be an online repository where supplementary codes and data can be stored.