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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

The minimum modulus of polynomials


Authors: E. Beller and D. J. Newman
Journal: Proc. Amer. Math. Soc. 45 (1974), 463-465
MSC: Primary 30A06
DOI: https://doi.org/10.1090/S0002-9939-1974-0355015-3
MathSciNet review: 0355015
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Abstract: In answer to a problem of Erdös and Littlewood we produce an $ n$th degree polynomial, $ P(z)$, with coefficients bounded by 1 satisfying $ \vert P(z)\vert > C\sqrt n $ for all $ z$ on $ \vert z\vert = 1$ ($ C$ is a positive absolute constant).


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DOI: https://doi.org/10.1090/S0002-9939-1974-0355015-3
Keywords: Polynomials, minimum modulus, Fourier series
Article copyright: © Copyright 1974 American Mathematical Society