Weber’s class number problem in the cyclotomic ℤ2-extension of ℚ, II

Takashi Fukuda, Keiichi Komatsu

    研究成果: Article

    6 引用 (Scopus)

    抄録

    Let hn denote the class number of n-th layer of the cyclotomic ℤ2-extension of ℚ. Weber proved that hn (n ≥ 1) is odd and Horie proved that hn (n ≥ 1) is not divisible by a prime number ℓ satisfying ℓ ≡ 3, 5 (mod 8). In a previous paper, the authors showed that hn (n ≥ 1) is not divisible by a prime number ℓ less than 107. In this paper, by investigating properties of a special unit more precisely, we show that hn (n ≥ 1) is not divisible by a prime number ℓ less than 1.2 • 108. Our argument also leads to the conclusion that hn (n ≥ 1) is not divisible by a prime number ℓ satisfying ℓ = ± 1 (mod 16).

    元の言語English
    ページ(範囲)359-368
    ページ数10
    ジャーナルJournal de Theorie des Nombres de Bordeaux
    22
    発行部数2
    DOI
    出版物ステータスPublished - 2010

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    Cyclotomic
    Class number
    Prime number
    Divisible
    Odd
    Denote
    Unit

    ASJC Scopus subject areas

    • Algebra and Number Theory

    これを引用

    Weber’s class number problem in the cyclotomic ℤ2-extension of ℚ, II. / Fukuda, Takashi; Komatsu, Keiichi.

    :: Journal de Theorie des Nombres de Bordeaux, 巻 22, 番号 2, 2010, p. 359-368.

    研究成果: Article

    Fukuda, Takashi ; Komatsu, Keiichi. / Weber’s class number problem in the cyclotomic ℤ2-extension of ℚ, II. :: Journal de Theorie des Nombres de Bordeaux. 2010 ; 巻 22, 番号 2. pp. 359-368.
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