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On the zeros of certain cosine polynomials


Authors: A. B. Mingarelli and S. Wang
Journal: Proc. Amer. Math. Soc. 118 (1993), 1103-1106
MSC: Primary 33B10; Secondary 42A05
MathSciNet review: 1137229
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Abstract: In a recent paper [The first sign change of a cosine polynomial, Proc. Amer. Math. Soc. 111 (1991), 709-716], Zeng studies the location of the first sign change of a cosine polynomial and thereby improves on results by Nulton and Stolarsky [The first sign change of a cosine polynomial, Proc. Amer. Math. Soc. 84 (1982), 55-59]. In this article we present a proof for each one of the four conjectures announced in Zeng's aforementioned paper and also discuss some extensions.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1137229-X
Keywords: Cosine polynomial, zeros, almost periodic functions, first sign change
Article copyright: © Copyright 1993 American Mathematical Society