The distribution of reduced numbers in an ideal of a real cubic number field
type: Item
instance of: scholarly article
title: The distribution of reduced numbers in an ideal of a real cubic number field
zbMATH Open document ID: 0567.12002
DOI: 10.1016/0022-314X(85)90037-X
published in: Journal of Number Theory
publication date: 1985-01-01T00:00:00Z
review text: According to the abstract of the author: ''Let K be a real but not totally real field of degree three over \({\mathbb{Q}}\), and let A be an ideal in K. It is proved that the reduced numbers in A (i.e., numbers \(\alpha\) with \(\alpha >1\) and \(-1<Re \alpha^{(j)}<0\) for all conjugates \(\alpha^{(j)}\neq \alpha)\) are dense in a set of intervals of constant length, and no reduced numbers in A occur in the gaps between these intervals. In fact, the intervals are determined explicitly, and criteria are given for when the reduced numbers in A actually are dense in the whole of \([1,\infty).\)''
Mathematics Subject Classification ID: 11R06
Mathematics Subject Classification ID: 11R16
Mathematics Subject Classification ID: 11R45
zbMATH DE Number: 3904699
zbMATH Keywords: cubic fields
zbMATH Keywords: density
zbMATH Keywords: ideal
zbMATH Keywords: reduced numbers
author: John Wolfskill
MaRDI profile type: Publication
cites work: Q3241280
cites work: Q5332701
cites work: On equivalence of binary forms
full work available at URL: 0022-314x(85)90037-x
OpenAlex ID: W2066921747
description: scientific article; zbMATH DE number 3904699