Prime divisors of sequences associated to elliptic curves

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

We consider the primes which divide the denominator of the x-coordinate of a sequence of rational points on an elliptic curve. It is expected that for every sufficiently large value of the index, each term should be divisible by a primitive prime divisor, one that has not appeared in any earlier term. Proofs of this are known in only a few cases. Weaker results in the general direction are given, using a strong form of Siegel's Theorem and some congruence arguments. Our main result is applied to the study of prime divisors of Somos sequences.

Keywords

Number Theory, 11G41; 11G05

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/70772

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0404129
 http://arxiv.org/abs/math/0404129

Collections

arXiv