Six unlikely intersection problems in search of effectivity
Number Theory
2016-08-03 v1
Abstract
We investigate four properties related to an elliptic curve in Legendre form with parameter : the curve has complex multiplication, has complex multiplication, a point on with abscissa is of finite order, and is a root of unity. Combining all pairs of properties leads to six problems on unlikely intersections. We solve these problems effectively and in certain cases also explicitly.
Cite
@article{arxiv.1509.06573,
title = {Six unlikely intersection problems in search of effectivity},
author = {P. Habegger and G. Jones and D. Masser},
journal= {arXiv preprint arXiv:1509.06573},
year = {2016}
}