Iwasawa invariants of real abelian number fields (Q1912276)

In this paper the author presents a criterion for the vanishing of the Iwasawa \(\lambda\)-invariant for the \(\mathbb{Z}_p\)-extension of a real abelian number field \(k\), where \(p\) is an odd prime. Using this criterion the following theorem (5.1) is proved: ``For \(m = 295, 397, 745\), or 1738, the \(\lambda\)-invariant \(\lambda\) of the cyclotomic \(\mathbb{Z}_3\)-extension of \(\mathbb{Q} (\sqrt m)\) is zero''.