A height inequality for rational points on elliptic curves implied by the abc-conjecture
Number Theory
2012-11-13 v2
Abstract
In this short note we show that the uniform abc-conjecture over number fields puts strong restrictions on the coordinates of rational points on elliptic curves. For the proof we use a variant of the uniform abc-conjecture over number fields formulated by Mochizuki. As an application, we generalize a result of Silverman on elliptic non-Wieferich primes.
Cite
@article{arxiv.1210.6543,
title = {A height inequality for rational points on elliptic curves implied by the abc-conjecture},
author = {Ulf Kühn and J. Steffen Müller},
journal= {arXiv preprint arXiv:1210.6543},
year = {2012}
}
Comments
6 pages. Fixed typos, added more references and an application to elliptic non-Wieferich primes