Rational points on X_0^+ (p^r)
Number Theory
2011-04-26 v1
Abstract
We show how the recent isogeny bounds due to \'E. Gaudron and G. R\'emond allow to obtain the triviality of X_0^+ (p^r)(Q), for r>1 and p a prime exceeding 2.10^{11}. This includes the case of the curves X_split (p). We then prove, with the help of computer calculations, that the same holds true for p in the range 10 < p < 10^{14}, p\neq 13. The combination of those results completes the qualitative study of such sets of rational points undertook in previous papers, with the exception of p=13.
Cite
@article{arxiv.1104.4641,
title = {Rational points on X_0^+ (p^r)},
author = {Yu. Bilu and P. Parent and M. Rebolledo},
journal= {arXiv preprint arXiv:1104.4641},
year = {2011}
}
Comments
16 pages, no figure