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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.

References [Enhancements On Off] (What's this?)

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Keywords: Newman polynomials, exponential sums
Article copyright: © Copyright 1992 American Mathematical Society

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