On Newman polynomials without roots on the unit circle
https://doi.org/10.22405/2226-8383-2019-20-1-195-201
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.
About the Author
Arturas Dubickas
Institute of Mathematics, Vilnius University, Vilnius (Lithuania)
Russian Federation
Russian Federation
habilitated doctor of mathematics, research professor
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Review
For citations:
Dubickas A. On Newman polynomials without roots on the unit circle. Chebyshevskii Sbornik. 2019;20(1):195-201. (In Russ.) https://doi.org/10.22405/2226-8383-2019-20-1-195-201
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