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

Takashi Fukuda, Keiichi Komatsu

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    7 Citations (Scopus)

    Abstract

    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).

    Original languageEnglish
    Pages (from-to)359-368
    Number of pages10
    JournalJournal de Theorie des Nombres de Bordeaux
    Volume22
    Issue number2
    DOIs
    Publication statusPublished - 2010

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    ASJC Scopus subject areas

    • Algebra and Number Theory

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