Root separation for reducible monic quartics
type: Item
instance of: scholarly article
title: Root separation for reducible monic quartics
zbMATH Open document ID: 1258.11052
DOI: 10.4171/RSMUP/126-4
author: Andrej Dujella
author: Tomislav Pejković
published in: Rendiconti del Seminario Matematico della Università di Padova
publication date: 2012-02-10T00:00:00Z
full work available at URL: https://eudml.org/doc/242958
full work available at URL: http://rendiconti.math.unipd.it/volumes/vol126.php
review text: For a polynomial \(P\) with integer coefficients one defines its height \(H(P)\), which is the maiximal modulus of its coefficients, and \(\text{sep}(P)\), the minimal distance between two distinct roots of it, and one puts \(\text{sep}(P)=H(P)^{-e(P)}\). There are still many open questions about the behaviour of \(e(P)\). Here the Authors prove that \(\limsup e(P)=2\) when \(P\) runs over all reducible monic quartic integer polynomials. This is the first case where an exact limit value of \(e(P)\) is proved for quartic polynomials. The proof is constructive.
reviewed by: Maurice Mignotte
Mathematics Subject Classification ID: 11C08
zbMATH DE Number: 6005070
MaRDI profile type: Publication
cites work: Q5433084
cites work: Root separation for irreducible integer polynomials
cites work: POLYNOMIAL ROOT SEPARATION
cites work: Q3023596
cites work: An inequality for the discriminant of a polynomial
cites work: Polynomial root separation examples
cites work: Q3645422
OpenAlex ID: W2002347766
description: scientific article; zbMATH DE number 6005070