On a family of quadratic fields whose class numbers are divisible by five (Q1281905)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: On a family of quadratic fields whose class numbers are divisible by five |
scientific article; zbMATH DE number 1268564
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On a family of quadratic fields whose class numbers are divisible by five |
scientific article; zbMATH DE number 1268564 |
Statements
On a family of quadratic fields whose class numbers are divisible by five (English)
0 references
25 November 1999
0 references
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.
0 references
quadratic fields
0 references
class numbers
0 references
