On number fields with an unramified abelian extension of degree \(2^{n+2}\)
type: Item
instance of: scholarly article
title: On number fields with an unramified abelian extension of degree \(2^{n+2}\)
zbMATH Open document ID: 0779.11048
author: Yizhong Lan
published in: Journal of Number Theory
publication date: 1993-08-17T00:00:00Z
review text: Let \(K\) be either a totally real or a totally imaginary number field. The author considers a special family of cubic polynomials \(f_ \lambda(x)\in K[x]\), each of which generates a cubic cyclic extension \(L\) of \(K\). For each \(L\) he is able to construct an unramified abelian extension of degree \(2^{n+2}\), where \(2^ n\) denotes the degree of the maximal unramified abelian 2-extension of \(K\). He makes the family of \(f_ \lambda(x)\) more explicit in the case that \(K\) is a quadratic field. In this case there is also a well-known lower bound for \(n\) coming from genus theory.
Mathematics Subject Classification ID: 11R20
Mathematics Subject Classification ID: 11R37
Mathematics Subject Classification ID: 11R11
zbMATH DE Number: 205451
zbMATH Keywords: quadratic extension
zbMATH Keywords: class field theory
zbMATH Keywords: unramified abelian extension
MaRDI profile type: Publication
full work available at URL: jnth.1993.1029
OpenAlex ID: W2016227038
DOI: 10.1006/JNTH.1993.1029
description: scientific article; zbMATH DE number 205451