On the Iwasawa $lambda$-invariants of cyclotomic $mathbb{Z}_{2}$-extensions of real abelian fields (Algebraic Number Theory and Related Topics 2014)

Abstract

Let p be a prime number and k a real abelian field. We denote by λp(k) the Iwasawa λ-invariant associated to the ideal class group of the cyclotomic Zp-extension of k. It is conjectured that λp(k) = 0. In [9], [10] and [11], Ichimura and Sumida discovered a good method for verifying that λp(k) = 0 for an odd prime number p. In this paper, we give a criterion for λ2(k) = 0, as a generalization of the preceding result [6]. Our criterion is considered as an even prime version of the theorem of Ichimura and Sumida.