CM-Points on Straight Lines
Number Theory
2014-10-31 v4
Abstract
We prove that, with "obvious" exceptions, a CM-point (j(\tau),j(\tau')) cannot belong to a straight line in C^2 defined over Q. This generalizes a result of K\"uhne, who proved this for the line x+y=1.
Cite
@article{arxiv.1406.1274,
title = {CM-Points on Straight Lines},
author = {Bill Allombert and Yuri Bilu and Amalia Pizarro-Madariaga},
journal= {arXiv preprint arXiv:1406.1274},
year = {2014}
}
Comments
Accepted for publication in "Analytic Number Theory" (dedicated do H. Maier), Springer, to appear