Proving the triviality of rational points on Atkin-Lehner quotients of Shimura curves
arXiv:0707.1330
Abstract
In this paper we give a method for studying global rational points on certain quotients of Shimura curves by Atkin-Lehner involutions. We obtain explicit conditions on such quotients for rational points to be ``trivial'' (coming from CM points only) and exhibit an explicit infinite family of such quotients satisfying these conditions.
25 pages. To appear in Mathematische Annalen