A Generalization of Siegel's Theorem and Hall's Conjecture

被引:3
作者
Everest, Graham [1 ]
Mahe, Valery [2 ]
机构
[1] Univ E Anglia, Sch Math, Norwich NR4 7TJ, Norfolk, England
[2] Inst Math & Modelisat Montpellier, F-34095 Montpellier, France
基金
英国工程与自然科学研究理事会;
关键词
Elliptic curve; Hall's conjecture; prime; Siegel's theorem; ELLIPTIC-CURVES; INTEGRAL POINTS;
D O I
10.1080/10586458.2009.10128889
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Consider an elliptic curve defined over the rational numbers and embedded in projective space. The rational points on the curve are viewed as integer vectors with coprime coordinates. What can be said about the rational points for which the number of prime factors dividing a fixed coordinate does not exceed a fixed bound? If the bound is zero, then Siegel's theorem guarantees that there are only finitely many such points. We consider, theoretically and computationally, two conjectures: one is a generalization of Siegel's theorem, and the other is a refinement that resonates with Hall's conjecture.
引用
收藏
页码:1 / 9
页数:9
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