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

Takashi Fukuda, Keiichi Komatsu

    研究成果: Article査読

    8 被引用数 (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).

    本文言語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
    2
    DOI
    出版ステータスPublished - 2010

    ASJC Scopus subject areas

    • Algebra and Number Theory

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