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Chebyshevskii Sbornik, 2019, Volume 20, Issue 1, Pages 197–203
DOI: https://doi.org/10.22405/2226-8383-2018-20-1-197-203
(Mi cheb726)
 

On Newman polynomials without roots on the unit circle

A. Dubickas

Institute of Mathematics, Vilnius University, Vilnius (Lithuania)
References:
Abstract: In this note we give a necessary and sufficient condition on the triplet of nonnegative integers $a<b<c$ for which the Newman polynomial $\sum_{j=0}^a x^j + \sum_{j=b}^c x^j$ has a root on the unit circle. From this condition we derive that for each $d \geq 3$ there is a positive integer $n>d$ such that the Newman polynomial $1+x+\dots+x^{d-2}+x^n$ of length $d$ has no roots on the unit circle.
Keywords: Newman polynomial, root of unity.
Received: 12.12.2018
Accepted: 10.04.2019
Document Type: Article
UDC: 512.62
Language: English
Citation: A. Dubickas, “On Newman polynomials without roots on the unit circle”, Chebyshevskii Sb., 20:1 (2019), 197–203
Citation in format AMSBIB
\Bibitem{Dub19}
\by A.~Dubickas
\paper On Newman polynomials without roots on the unit circle
\jour Chebyshevskii Sb.
\yr 2019
\vol 20
\issue 1
\pages 197--203
\mathnet{http://mi.mathnet.ru/cheb726}
\crossref{https://doi.org/10.22405/2226-8383-2018-20-1-197-203}
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