Class number calculation using Siegel functions

T. Fukuda, Keiichi Komatsu

    Research output: Contribution to journalArticle

    Abstract

    We propose a fast method of calculating the p-part of the class numbers in certain non-cyclotomic ℤp-extensions of an imaginary quadratic field using elliptic units constructed by Siegel functions. We carried out practical calculations for p=3 and determined λ-invariants of such ℤ3-extensions which were not known in our previous paper.

    Original languageEnglish
    Pages (from-to)295-302
    Number of pages8
    JournalLMS Journal of Computation and Mathematics
    Volume17
    Issue numberSPEC. ISSUE A
    DOIs
    Publication statusPublished - 2014

    Fingerprint

    Class number
    Imaginary Quadratic Field
    Unit
    Invariant

    ASJC Scopus subject areas

    • Mathematics(all)
    • Computational Theory and Mathematics

    Cite this

    Class number calculation using Siegel functions. / Fukuda, T.; Komatsu, Keiichi.

    In: LMS Journal of Computation and Mathematics, Vol. 17, No. SPEC. ISSUE A, 2014, p. 295-302.

    Research output: Contribution to journalArticle

    Fukuda, T. ; Komatsu, Keiichi. / Class number calculation using Siegel functions. In: LMS Journal of Computation and Mathematics. 2014 ; Vol. 17, No. SPEC. ISSUE A. pp. 295-302.
    @article{dc5ce855521446aa9f04bea7a927c57c,
    title = "Class number calculation using Siegel functions",
    abstract = "We propose a fast method of calculating the p-part of the class numbers in certain non-cyclotomic ℤp-extensions of an imaginary quadratic field using elliptic units constructed by Siegel functions. We carried out practical calculations for p=3 and determined λ-invariants of such ℤ3-extensions which were not known in our previous paper.",
    author = "T. Fukuda and Keiichi Komatsu",
    year = "2014",
    doi = "10.1112/S146115701400014X",
    language = "English",
    volume = "17",
    pages = "295--302",
    journal = "LMS Journal of Computation and Mathematics",
    issn = "1461-1570",
    publisher = "London Mathematical Society",
    number = "SPEC. ISSUE A",

    }

    TY - JOUR

    T1 - Class number calculation using Siegel functions

    AU - Fukuda, T.

    AU - Komatsu, Keiichi

    PY - 2014

    Y1 - 2014

    N2 - We propose a fast method of calculating the p-part of the class numbers in certain non-cyclotomic ℤp-extensions of an imaginary quadratic field using elliptic units constructed by Siegel functions. We carried out practical calculations for p=3 and determined λ-invariants of such ℤ3-extensions which were not known in our previous paper.

    AB - We propose a fast method of calculating the p-part of the class numbers in certain non-cyclotomic ℤp-extensions of an imaginary quadratic field using elliptic units constructed by Siegel functions. We carried out practical calculations for p=3 and determined λ-invariants of such ℤ3-extensions which were not known in our previous paper.

    UR - http://www.scopus.com/inward/record.url?scp=84905459615&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=84905459615&partnerID=8YFLogxK

    U2 - 10.1112/S146115701400014X

    DO - 10.1112/S146115701400014X

    M3 - Article

    VL - 17

    SP - 295

    EP - 302

    JO - LMS Journal of Computation and Mathematics

    JF - LMS Journal of Computation and Mathematics

    SN - 1461-1570

    IS - SPEC. ISSUE A

    ER -