A remark on the class number of the maximal real subfield of a cyclotomic field. II
[Part I, cf. ibid. 65, No. 9, 318-319 (1989; Zbl 0704.11039).] In this paper, the author considers the class number \(h_ K\) of the maximal real subfield \(K\) of a cyclotomic field \(\mathbb{Q}(\zeta_ q)\) with prime \(q\) satisfying \(q=4p+1\) for a prime \(p\) and the class number \(h_ F\) of the real quadratic subfield \(\mathbb{Q}(\sqrt{q})=F\), and proves by purely algebraic method that \(h_ K=h_ F\) holds if \(h_ K<q\), \(p+1\) is not a power of 2 and \(2p+1\) is not a power of 3. For a review of Part III (see below).
scientific article; zbMATH DE number 97925