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

Takashi Fukuda, Keiichi Komatsu

    Research output: Contribution to journalArticle

    11 Citations (Scopus)

    Abstract

    Let hn denote the class number of ℚ(2cos(27π/2 n+2)). Weber proved that hn is odd for all n ≥ 1. We claim that if I is a prime number less than 107, then for all n≥ 1, ℓ does not divide hn.

    Original languageEnglish
    Pages (from-to)213-222
    Number of pages10
    JournalExperimental Mathematics
    Volume18
    Issue number2
    Publication statusPublished - 2009

    Fingerprint

    Cyclotomic
    Class number
    Prime number
    Divides
    Odd
    Denote

    Keywords

    • Class number
    • Computation

    ASJC Scopus subject areas

    • Mathematics(all)

    Cite this

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

    In: Experimental Mathematics, Vol. 18, No. 2, 2009, p. 213-222.

    Research output: Contribution to journalArticle

    Fukuda, T & Komatsu, K 2009, 'Weber's class number problem in the cyclotomic ℤ2-extension of ℚ', Experimental Mathematics, vol. 18, no. 2, pp. 213-222.
    Fukuda, Takashi ; Komatsu, Keiichi. / Weber's class number problem in the cyclotomic ℤ2-extension of ℚ. In: Experimental Mathematics. 2009 ; Vol. 18, No. 2. pp. 213-222.
    @article{6c5ba9d8b8c54a659600a94b4563cab0,
    title = "Weber's class number problem in the cyclotomic ℤ2-extension of ℚ",
    abstract = "Let hn denote the class number of ℚ(2cos(27π/2 n+2)). Weber proved that hn is odd for all n ≥ 1. We claim that if I is a prime number less than 107, then for all n≥ 1, ℓ does not divide hn.",
    keywords = "Class number, Computation",
    author = "Takashi Fukuda and Keiichi Komatsu",
    year = "2009",
    language = "English",
    volume = "18",
    pages = "213--222",
    journal = "Experimental Mathematics",
    issn = "1058-6458",
    publisher = "A K Peters",
    number = "2",

    }

    TY - JOUR

    T1 - Weber's class number problem in the cyclotomic ℤ2-extension of ℚ

    AU - Fukuda, Takashi

    AU - Komatsu, Keiichi

    PY - 2009

    Y1 - 2009

    N2 - Let hn denote the class number of ℚ(2cos(27π/2 n+2)). Weber proved that hn is odd for all n ≥ 1. We claim that if I is a prime number less than 107, then for all n≥ 1, ℓ does not divide hn.

    AB - Let hn denote the class number of ℚ(2cos(27π/2 n+2)). Weber proved that hn is odd for all n ≥ 1. We claim that if I is a prime number less than 107, then for all n≥ 1, ℓ does not divide hn.

    KW - Class number

    KW - Computation

    UR - http://www.scopus.com/inward/record.url?scp=68949110186&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=68949110186&partnerID=8YFLogxK

    M3 - Article

    AN - SCOPUS:68949110186

    VL - 18

    SP - 213

    EP - 222

    JO - Experimental Mathematics

    JF - Experimental Mathematics

    SN - 1058-6458

    IS - 2

    ER -