An inequality about irreducible factors of integer polynomials
type: Item
instance of: scholarly article
title: An inequality about irreducible factors of integer polynomials
zbMATH Open document ID: 0648.12002
DOI: 10.1016/0022-314X(88)90014-5
author: Maurice Mignotte
published in: Journal of Number Theory
publication date: 1988-01-01T00:00:00Z
review text: Let \(F(X)=a_0+a_1X+a_2X^2+ \ldots +a_dX^d\) be a polynomial of degree \(d\) with complex coefficients. The author gives an upper bound for \(\max \{| F(z)|: | z| =1\}\) in the case when \(F(X)\) is an irreducible polynomial with integral coefficients. The upper bound involves the measure of \(F\), namely, \(M(F)=| a_d| \prod^{d}_{j=1} \max \{1, |z_j|\}\), where \(z_1,\ldots, z_d\) are the complex roots of \(F\). A special case of the author's result is the following inequality: \[ \left(\sum^d_{i=0}| a_i|^2\right)^{1/2}\le e^{\sqrt{d}}(d+2\sqrt{d}+2)^{1+\sqrt{d}}M(F)^{1+\sqrt{d}}. \]
reviewed by: Kenneth S. Williams
Mathematics Subject Classification ID: 11R09
Mathematics Subject Classification ID: 11C08
zbMATH DE Number: 4057625
zbMATH Keywords: measure of polynomial
zbMATH Keywords: inequality
zbMATH Keywords: irreducible factors of integer polynomials
MaRDI profile type: Publication
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full work available at URL: 0022-314x(88)90014-5
OpenAlex ID: W2021305840
description: scientific article; zbMATH DE number 4057625