An effective bound of $p$ for algebraic points on Shimura curves of ${\Gamma }_0(p)$-type

Abstract

In previous articles, we classified the characters associated to algebraic points on Shimura curves of ${\Gamma }_0(p)$-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 $p$. In this article, we obtain an effective bound of $p$ concerning algebraic points on Shimura curves of ${\Gamma }_0(p)$-type.

11 pages. arXiv admin note: substantial text overlap with arXiv:1205.3596, arXiv:1202.4841