A Generalization of Siegel's Theorem and Hall's Conjecture - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Experimental Mathematics Année : 2009

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

Résumé

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 a rational point if a bound is placed upon the number of prime factors dividing a fixed coordinate? 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 which resonates with Hall's conjecture.

Dates et versions

hal-00482447 , version 1 (10-05-2010)

Identifiants

Citer

Graham Everest, Valery Mahe. A Generalization of Siegel's Theorem and Hall's Conjecture. Experimental Mathematics, 2009, 18 (1), pp.1 -- 9. ⟨10.1080/10586458.2009.10128889⟩. ⟨hal-00482447⟩
40 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More