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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Finite exponential series and Newman polynomials


Author: Bart Goddard
Journal: Proc. Amer. Math. Soc. 116 (1992), 313-320
MSC: Primary 11L03; Secondary 30C10
MathSciNet review: 1101984
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Abstract: A Newman polynomial is a sum of powers of $ z$, with constant term 1. The Newman polynomial of four terms whose minimum modulus on the unit circle is as large as possible is found by examining the expression

$\displaystyle f(4) = \mathop {\sup }\limits_{{x_1} < \cdots < {x_4}} \mathop {\... ...\in \Re } \left\vert {\sum\limits_{j = 1}^4 {{e^{i{x_j}\alpha }}} } \right\vert$

and determining an extremal system $ ({x_1}, \ldots ,{x_4})$ using a technique that reduces the problem to a finite search.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1992-1101984-4
PII: S 0002-9939(1992)1101984-4
Keywords: Newman polynomials, exponential sums
Article copyright: © Copyright 1992 American Mathematical Society