Algebraic points on Shimura curves of $\Gamma_0(p)$-type (III)
Number Theory
2013-03-22 v1
Abstract
In previous articles, we classified the characters associated to algebraic points on Shimura curves of -type, and over number fields in a certain large class we showed that there are at most elliptic points on such a Shimura curve for every sufficiently large prime number . In this article, we prove the non-existence of elliptic points on Shimura curves of -type under a mild assumption. We also give an explicit example.
Keywords
Cite
@article{arxiv.1303.5270,
title = {Algebraic points on Shimura curves of $\Gamma_0(p)$-type (III)},
author = {Keisuke Arai},
journal= {arXiv preprint arXiv:1303.5270},
year = {2013}
}
Comments
11 pages. arXiv admin note: substantial text overlap with arXiv:1211.0129, arXiv:1205.3596, arXiv:1202.4841