Weber's class number problem in the cyclotomic Z2-extension of Q III

Takashi Fukuda, Keiichi Komatsu

    Research output: Contribution to journalArticle

    11 Citations (Scopus)

    Abstract

    Let hn denote the class number of Q(2 cos2π/2n+2) which is a cyclic extension of degree 2n over the rational number field Q. There are no known examples of hn > 1. We prove that a prime number ℓ does not divide hn for all n < 1 if ℓ is less than 109 or ℓ satisfies a congruence relation ℓ ≢ ± 1 (mod 32).

    Original languageEnglish
    Pages (from-to)1627-1635
    Number of pages9
    JournalInternational Journal of Number Theory
    Volume7
    Issue number6
    DOIs
    Publication statusPublished - 2011 Sep

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    Congruence Relation
    Cyclotomic
    Class number
    Prime number
    Number field
    Divides
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    Keywords

    • Class number
    • computation

    ASJC Scopus subject areas

    • Algebra and Number Theory

    Cite this

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

    In: International Journal of Number Theory, Vol. 7, No. 6, 09.2011, p. 1627-1635.

    Research output: Contribution to journalArticle

    Fukuda, Takashi ; Komatsu, Keiichi. / Weber's class number problem in the cyclotomic Z2-extension of Q III. In: International Journal of Number Theory. 2011 ; Vol. 7, No. 6. pp. 1627-1635.
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