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On Newman polynomials without roots on the unit circle
A. Dubickas Institute of Mathematics, Vilnius University, Vilnius (Lithuania)
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
Citation:
A. Dubickas, “On Newman polynomials without roots on the unit circle”, Chebyshevskii Sb., 20:1 (2019), 197–203
Linking options:
https://www.mathnet.ru/eng/cheb726 https://www.mathnet.ru/eng/cheb/v20/i1/p197
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Abstract page: | 114 | Full-text PDF : | 38 | References: | 27 |
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