Uchida, Kôji Class numbers of cubic cyclic fields. (English) Zbl 0281.12007 J. Math. Soc. Japan 26, 447-453 (1974). Let \(n\) be any given positive integer. It is known that there exist real (imaginary) quadratic fields whose class numbers are divisible by \(n\). This is classical for the imaginary case and the real case was proved by Y. Yamamoto [ Osaka J. Math. 7, 57–76 (1970; Zbl 0222.12003)]. It is shown in this paper that the same is true for cubic cyclic fields. We deal with fields defined by equations \(X^3+pX^2+2pX+p=0\) for integers \(p\) and special properties of these equations play essential roles. Reviewer: Kôji Uchida (Sendai) Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 7 ReviewsCited in 17 Documents MSC: 11R29 Class numbers, class groups, discriminants 11R16 Cubic and quartic extensions 11R20 Other abelian and metabelian extensions Citations:Zbl 0222.12003 PDF BibTeX XML Cite \textit{K. Uchida}, J. Math. Soc. Japan 26, 447--453 (1974; Zbl 0281.12007) Full Text: DOI OpenURL