TY - JOUR
T1 - On the Iwasawa λ-invariant of the cyclotomic Z2-extension of Q(√p), III
AU - Fukuda, Takashi
AU - Komatsu, Keiichi
AU - Ozaki, Manabu
AU - Tsuji, Takae
PY - 2016
Y1 - 2016
N2 - 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.
AB - 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.
KW - Cyclotomic unit
KW - Iwasawa invariant
KW - Real quadratic field
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U2 - 10.7169/facm/2016.54.1.1
DO - 10.7169/facm/2016.54.1.1
M3 - Article
AN - SCOPUS:84962124272
VL - 54
SP - 7
EP - 17
JO - Functiones et Approximatio, Commentarii Mathematici
JF - Functiones et Approximatio, Commentarii Mathematici
SN - 0208-6573
IS - 1
ER -