Class numbers of cubic cyclic fields
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 \textit{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.
scientific article; zbMATH DE number 3440521