On denominators of algebraic numbers and integer polynomials
type: Item
instance of: scholarly article
title: On denominators of algebraic numbers and integer polynomials
zbMATH Open document ID: 0866.11059
author: Steven Arno
author: M. L. Robinson
author: Ferell S. Wheeler
published in: Journal of Number Theory
publication date: 1997-08-03T00:00:00Z
review text: Let \(\alpha\) be an algebraic number with minimal polynomial \(a_dX^d+\cdots+ a_0\in[X]\). The denominator \(\text{den}(\alpha)\) of \(\alpha\) is the least positive integer \(n\) for which \(n\alpha\) is an algebraic integer. It is well known that this integer \(\text{den}(\alpha)\) divides \(a_d\). The authors compute the density of algebraic numbers \(\alpha\) of a given degree \(d\) such that \(\text{den}(\alpha)=a_d\). This density is asymptotic to \(1/\zeta(3)\) when \(d\) tends to infinity.
reviewed by: Michel Waldschmidt
Mathematics Subject Classification ID: 11R04
Mathematics Subject Classification ID: 11R09
zbMATH DE Number: 874197
zbMATH Keywords: algebraic numbers
zbMATH Keywords: denominator
zbMATH Keywords: density
MaRDI profile type: Publication
full work available at URL: jnth.1996.0049
OpenAlex ID: W2087622616
DOI: 10.1006/JNTH.1996.0049
description: scientific article; zbMATH DE number 874197