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An effective bound of $p$ for algebraic points on Shimura curves of $\varGamma _{0}(p)$-type

Volume 164 / 2014

Keisuke Arai Acta Arithmetica 164 (2014), 343-353 MSC: Primary 11G18, 14G05; Secondary 11G10, 11G15. DOI: 10.4064/aa164-4-2

Abstract

In previous articles, we showed that for number fields in a certain large class, there are at most elliptic points on a Shimura curve of $\varGamma _0(p)$-type for every sufficiently large prime number $p$. In this article, we obtain an effective bound for such $p$.

Authors

  • Keisuke AraiDepartment of Mathematics
    School of Engineering
    Tokyo Denki University
    5 Senju Asahi-cho
    Adachi-ku, Tokyo 120-8551, Japan
    e-mail

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