A converse of Artin's density theorem: The case of cubic fields
type: Item
instance of: scholarly article
title: A converse of Artin's density theorem: The case of cubic fields
zbMATH Open document ID: 0779.11047
author: Ilaria Del Corso
author: Roberto Dvornicich
published in: Journal of Number Theory
publication date: 1993-10-18T00:00:00Z
review text: For fixed \(n\) consider the sequence \({\mathcal A}\) of all algebraic integers of degree \(n\), ordered according to the height of the minimal polynomials. For any prime \(p\) consider the subsequence \({\mathcal A}(p,\Phi)\) of \({\mathcal A}\) formed by algebraic integers generating a field in which \(p\) factorizes into prime ideals in a prescribed manner \(\Phi\). The authors show that \({\mathcal A}(p,\Phi)\) has always a natural density in \({\mathcal A}\) and compute it explicitly in the case of \(n=3\).
reviewed by: Władysław Narkiewicz
Mathematics Subject Classification ID: 11R16
Mathematics Subject Classification ID: 11R45
zbMATH DE Number: 431337
zbMATH Keywords: cubic fields
zbMATH Keywords: splitting of primes
zbMATH Keywords: algebraic integers
zbMATH Keywords: minimal polynomials
MaRDI profile type: Publication
full work available at URL: jnth.1993.1063
OpenAlex ID: W2061893548
DOI: 10.1006/JNTH.1993.1063
description: scientific article; zbMATH DE number 431337