On \({\mathbb{Z}}_ p\)-extensions of real abelian fields
The author intends to show that a result on \({\mathbb{Z}}_ p\)-extensions of real quadratic fields obtained by \textit{T. Fukuda} and \textit{K. Komatsu} [J. Number Theory 23, 238-242 (1986; Zbl 0593.12003)] can be extended in a real abelian case. Namely, let k be a finite abelian extension of rationals \({\mathbb{Q}}\) and p be an odd prime number splitting completely in k. Then, any \({\mathbb{Z}}_ p\)-extension K/k is cyclotomic. The author gives a sufficient condition for the Iwasawa invariant \(\lambda_ p(k)\) of k to vanish under the assumption \((h_ k,p)=1\) for the class number \(h_ k\) of k.
scientific article; zbMATH DE number 4142153