Ichimura-Sumida criterion for Iwasawa \(\lambda\)-invariants (Q1594775)

Let \(p\) be an odd prime number and \(k\) a cyclic extension of \({\mathbb Q}\) of degree \(p\). The main theorem gives a criterion for the vanishing of the Iwasawa invariant \(\lambda\) for the cyclotomic \({\mathbb Z}_p\) extension of \(k\) in terms of cyclotomic units in the case where \(p\) splits completely in \(k/{\mathbb Q}\). The authors conclude the note by numerical examples. In particular, they show the vanishing of \(\lambda\) for \textbf{all} cyclic cubic fields of prime conductor less than 10.000.