Torsion points with multiplicatively dependent coordinates on elliptic curves

被引：5

作者：

Barroero, Fabrizio ^{[1
]}

Sha, Min ^{[2
]}

机构：

[1] Univ Roma Tre, Dipartimento Matemat & Fis, Largo San Murialdo 1, I-00146 Rome, Italy

[2] Macquarie Univ, Dept Comp, Balaclava Rd, Sydney, NSW 2109, Australia

来源：

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY | 2020年 / 52卷 / 05期

关键词：

11G05; 11G50; 11U09; 14K05 (primary); RATIONAL-POINTS; UNLIKELY INTERSECTIONS; SMALL HEIGHT; FAMILIES; CONJECTURE; PRODUCTS;

D O I：

10.1112/blms.12363

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study the finiteness problem of torsion points on an elliptic curve whose coordinates satisfy some multiplicative dependence relations. In particular, we prove that on an elliptic curve defined over a number field there are only finitely many torsion points whose coordinates are multiplicatively dependent. Moreover, we produce an effective result when the elliptic curve is defined over the rational numbers or has complex multiplication.

引用

页码：807 / 815

页数：9

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