To the Hilbert class field from the hypergeometric modular function

A. Nagano, H. Shiga*

*この研究の対応する著者

    研究成果: Article査読

    2 被引用数 (Scopus)

    抄録

    In this article we make an explicit approach to the problem: "For a given CM field M, construct its maximal unramified abelian extension C(M) by the adjunction of special values of certain modular functions" in some restricted cases with [M: Q] ≥ 4. We make our argument based on Shimura's main result on the complex multiplication theory of his article in 1967. His main result treats CM fields embedded in a quaternion algebra B over a totally real number field F. We determine the modular function which gives the canonical model for all B's coming from arithmetic triangle groups. That is our main theorem. As its application, we make an explicit case-study for B corresponding to the arithmetic triangle group δ(3, 3, 5). By using the modular function of K. Koike obtained in 2003, we show several examples of the Hilbert class fields as an application of our theorem to this triangle group.

    本文言語English
    ページ(範囲)408-430
    ページ数23
    ジャーナルJournal of Number Theory
    165
    DOI
    出版ステータスPublished - 2016 8 1

    ASJC Scopus subject areas

    • 代数と数論

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