On the Iwasawa λ-invariant of the cyclotomic Z2-extension of Q(√p), III

Takashi Fukuda, Keiichi Komatsu, Manabu Ozaki, Takae Tsuji

    Research output: Contribution to journalArticle

    1 Citation (Scopus)

    Abstract

    In the preceding papers, two of authors developed criteria for Greenberg conjecture of the cyclotomic Z2-extension of k = Q(√p ) with prime number p. Criteria and numerical algorithm in [5], [3] and [6] enable us to show λ2(k) = 0 for all p less than 105 except p =13841; 67073. All the known criteria at present can not handle p = 13841; 67073. In this paper, we develop another criterion for λ2(k) = 0 using cyclotomic units and Iwasawa polynomials, which is considered a slight modification of the method of Ichimura and Sumida. Our new criterion fits the numerical examination and quickly shows that λ2(Q(√p )) = 0 for p = 13841; 67073. So we announce here that λ2(Q(√p)) = 0 for all prime numbers p less that 105.

    Original languageEnglish
    Pages (from-to)7-17
    Number of pages11
    JournalFunctiones et Approximatio, Commentarii Mathematici
    Volume54
    Issue number1
    DOIs
    Publication statusPublished - 2016

      Fingerprint

    Keywords

    • Cyclotomic unit
    • Iwasawa invariant
    • Real quadratic field

    ASJC Scopus subject areas

    • Mathematics(all)

    Cite this