On a family of quadratic fields whose class numbers are divisible by five
The author presents a parametrized family of quadratic fields \(\Gamma\) the class numbers of which are divisible by 5. He uses a family of quintic polynomials introduced by \textit{T. Kondo} [On a family of sextic polynomials found by Brumer, Proc. 2nd Symp. on Number Theory, Tsuda Coll., pp. 27-36 (1997)]. If these polynomials are irreducible, their roots generate cyclic or dihedral extensions. For a suitable choice of parameters their corresponding Galois closures are \(D_5\) and they are unramified over the quadratic subfield.
scientific article; zbMATH DE number 1268564