Finite exponential series and Newman polynomials

Goddard, Bart

doi:10.1090/S0002-9939-1992-1101984-4

Finite exponential series and Newman polynomials
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by Bart Goddard PDF

Proc. Amer. Math. Soc. 116 (1992), 313-320 Request permission

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 \[ f(4) = \sup \limits _{{x_1} < \cdots < {x_4}} \inf \limits _{\alpha \in \Re } \left | {\sum \limits _{j = 1}^4 {{e^{i{x_j}\alpha }}} } \right |\] 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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