Let k=Q((D 2+md)(D 2+nd)(D 2+rd)), this paper proves firstly that the fundamental unit of k is ε=((D 2+md)(D 2+nd)+D 2(D 2+rd)) 2/(|mn|d 2), where D,d,m,n, and r are rational integers satisfying certain cond...Let k=Q((D 2+md)(D 2+nd)(D 2+rd)), this paper proves firstly that the fundamental unit of k is ε=((D 2+md)(D 2+nd)+D 2(D 2+rd)) 2/(|mn|d 2), where D,d,m,n, and r are rational integers satisfying certain conditions. Consequently, we describe the fundamental unit system of K=Q(D 2+md,D 2+nd,D 2+rd) explicitly by the fundamental unit of all the quadratic subfields and the class number h K explicitly by the class numbers of all the quadratic subfields. We also provide the fundamental unit system of some fields of (2,2) type.展开更多
文摘Let k=Q((D 2+md)(D 2+nd)(D 2+rd)), this paper proves firstly that the fundamental unit of k is ε=((D 2+md)(D 2+nd)+D 2(D 2+rd)) 2/(|mn|d 2), where D,d,m,n, and r are rational integers satisfying certain conditions. Consequently, we describe the fundamental unit system of K=Q(D 2+md,D 2+nd,D 2+rd) explicitly by the fundamental unit of all the quadratic subfields and the class number h K explicitly by the class numbers of all the quadratic subfields. We also provide the fundamental unit system of some fields of (2,2) type.
