On the use of explicit bounds on residues of Dedekind zeta functions taking into account the behavior of small primes
type: Item
instance of: scholarly article
title: On the use of explicit bounds on residues of Dedekind zeta functions taking into account the behavior of small primes
zbMATH Open document ID: 1091.11039
published in: Journal de Théorie des Nombres de Bordeaux
publication date: 2006-03-30T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/52468
review text: For a number field \(K\), one can improve known explicit bounds of the residue at \(s=1\) of the Dedekind zeta function \(\zeta_K(s)\) by taking into account the factorization behavior of a few small primes. The author shows how this can be applied to obtain better lower bounds for relative class numbers of CM-fields. In particular he deals with the so-called simplest cubic and simplest quartic fields, providing examples of these fields with exceptionally large class numbers. In this way he finds examples of cyclotomic fields with prime conductor and a large plus factor of the class number. Other applications concern imaginary cyclic quartic fields with ideal class groups of exponent 1 or 2 and also some non-abelian fields.
Mathematics Subject Classification ID: 11R29
Mathematics Subject Classification ID: 11R16
Mathematics Subject Classification ID: 11R18
Mathematics Subject Classification ID: 11R42
zbMATH DE Number: 5016575
zbMATH Keywords: Class numbers
zbMATH Keywords: cubic and quartic extensions
zbMATH Keywords: cyclotomic fields
zbMATH Keywords: zeta functions
author: Stéphane Louboutin
MaRDI profile type: Publication
OpenAlex ID: W1976383277
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DOI: 10.5802/JTNB.508
description: scientific article; zbMATH DE number 5016575