Integral points on elliptic curves and 3-torsion in class groups
Number Theory
2007-05-23 v2
Abstract
We give new bounds for the number of integral points on elliptic curves. The method may be said to interpolate between approaches via diophantine techniques ([BP], [HBR]) and methods based on quasiorthogonality in the Mordell-Weil lattice ([Sil6], [GS], [He]). We apply our results to break previous bounds on the number of elliptic curves of given conductor and the size of the 3-torsion part of the class group of a quadratic field. The same ideas can be used to count rational points on curves of higher genus.
Cite
@article{arxiv.math/0405180,
title = {Integral points on elliptic curves and 3-torsion in class groups},
author = {H. A. Helfgott and A. Venkatesh},
journal= {arXiv preprint arXiv:math/0405180},
year = {2007}
}
Comments
23 pages, no figures, v2. To appear in J. Amer. Math. Soc