On a family of quadratic fields whose class numbers are divisible by five
type: Item
instance of: scholarly article
title: On a family of quadratic fields whose class numbers are divisible by five
zbMATH Open document ID: 0926.11081
author: Masahiko Sase
published in: Proceedings of the Japan Academy. Series A
publication date: 1999-11-25T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 11R11
Mathematics Subject Classification ID: 11R29
zbMATH DE Number: 1268564
zbMATH Keywords: quadratic fields
zbMATH Keywords: class numbers
reviewed by: Michael E. Pohst
MaRDI profile type: Publication
full work available at URL: pjaa.74.120
OpenAlex ID: W2031854718
cites work: Parametrization of the quadratic fields whose class numbers are divisible by three
cites work: Effective Determination of the Decomposition of the Rational Primes in a Cubic Field
cites work: Solving Solvable Quintics
cites work: Q3139838
DOI: 10.3792/PJAA.74.120
description: scientific article; zbMATH DE number 1268564