Dihedral and cyclic extensions with large class numbers
type: Item
instance of: scholarly article
title: Dihedral and cyclic extensions with large class numbers
zbMATH Open document ID: 1275.11145
author: Henry H. Kim
author: Peter Jaehyun Cho
published in: Journal de Théorie des Nombres de Bordeaux
publication date: 2013-03-07T00:00:00Z
review text: The authors construct unconditionally families of number fields with large class numbers whose Galois closures have as Galois groups: dihedral groups \(D_n\), where \(n=3,4,5\), or cyclic groups \(C_ n\), where \(n=4,5,6\). They first construct families of number fields with small regulators, and by using the strong Artin conjecture and applying some modification of zero density result in [\textit{E. Kowalski} and \textit{P. Michel}, Pac. J. Math. 207, No. 2, 411--431 (2002; Zbl 1129.11316)] they choose subfamilies such that the corresponding \(L\)-functions are zero free close to \(1\). For these subfamilies, the L-functions have the extremal value at \(s=1\), and by the class number formula, they obtain large class numbers. This paper is a continuation of \textit{P. J. Cho} and \textit{H. H. Kim} [Can. J. Math. 65, No. 6, 1201--1216 (2013; Zbl 1283.11155)].
reviewed by: Bouchaïb Sodaïgui
Mathematics Subject Classification ID: 11R29
Mathematics Subject Classification ID: 11R32
Mathematics Subject Classification ID: 11R42
Mathematics Subject Classification ID: 11R21
zbMATH DE Number: 6142425
zbMATH Keywords: class number
zbMATH Keywords: dihedral and cyclic extensions
zbMATH Keywords: L-functions
MaRDI profile type: Publication
OpenAlex ID: W2317436263
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DOI: 10.5802/JTNB.812
description: scientific article; zbMATH DE number 6142425