Unit groups and Iwasawa lambda invariants of some multiquadratic number fields. (English) Zbl 1468.11223

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 \(p_1\equiv7\pmod{16}, p_2\equiv3\pmod8\).


11R20 Other abelian and metabelian extensions
11R04 Algebraic numbers; rings of algebraic integers
11R23 Iwasawa theory
11R27 Units and factorization
11R29 Class numbers, class groups, discriminants
Full Text: DOI


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