Polynomials with all zeros on the unit circle
type: Item
instance of: scholarly article
title: Polynomials with all zeros on the unit circle
zbMATH Open document ID: 1224.26055
author: Piroska Lakatos
author: László Losonczi
published in: Acta Mathematica Hungarica
publication date: 2011-02-08T00:00:00Z
review text: A univariate polynomial \(p(z)=\sum_{k=0}^m A_k z^k \in {\mathbb C}[z]\) is called self-inversive if there exists \(\theta \in {\mathbb R}\) such that \(A_{m-k} = e^{i\theta} \bar{A}_k\) for all \(k\). The authors give a sufficient condition for all the zeros of a self-inversive polynomial to lie on the unit circle. The condition is piecewise-linear and depends on three complex parameters to be found.
reviewed by: Didier Henrion
Mathematics Subject Classification ID: 26C10
Mathematics Subject Classification ID: 30C15
zbMATH DE Number: 5848608
zbMATH Keywords: self-inversive polynomial
zbMATH Keywords: zeros on the unit circle
MaRDI profile type: Publication
full work available at URL: s10474-009-9028-7
OpenAlex ID: W2081845331
cites work: Properties of line spectrum pair polynomials. A review
cites work: Zeros of Self-Inversive Polynomials
cites work: Construction of unitary and normal companion matrices
cites work: On the zeros of certain self-reciprocal polynomials
cites work: Q4795324
cites work: Q4821446
cites work: Q3023601
cites work: Circular interlacing with reciprocal polynomials
cites work: Self-inversive polynomials of odd degree
cites work: Q5546070
cites work: Q4861743
cites work: Littlewood Pisot numbers
cites work: Q5536376
cites work: Q3257783
cites work: Self-inversive polynomials with all zeros on the unit circle
DOI: 10.1007/S10474-009-9028-7
description: scientific article; zbMATH DE number 5848608