Unit groups and Iwasawa lambda invariants of some multiquadratic number fields (Q2024028)

The authors consider the field \(L=\mathbb Q(\sqrt{q_1},\sqrt{q_2},\sqrt2,i)\), where \(q_1,q_2\) are primes satisfying \(q_1\equiv 7\pmod 8, q_2\equiv3\pmod 8\) and determine the fundamental units and the \(2\)-class-group of \(L\) and its maximal real subfield. As an application they show that the Iwasawa coefficient \(\lambda(F)\) equals three for the cyclotomic \(\mathbb Z_2\)-extension of \(F=\mathbb Q(\sqrt{p_1},\sqrt{p_2},i)\), where \(p_1,p_2\) are primes with \(p_1\equiv7\pmod{16}, p_2\equiv3\pmod8\).