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

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.