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The minimum modulus of polynomials

Published:1974 Issue:3 Volume:45 Page:463-465
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Beller E.,Newman D. J.

Abstract

In answer to a problem of Erdös and Littlewood we produce an n n th degree polynomial, P ( z ) P(z) , with coefficients bounded by 1 satisfying | P ( z ) | > C n |P(z)| > C\sqrt n for all z z on | z | = 1 |z| = 1 ( C C is a positive absolute constant).

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1974-045-03/S0002-9939-1974-0355015-3/S0002-9939-1974-0355015-3.pdf

Reference4 articles.

1. An 𝑙₁ extremal problem for polynomials;Beller, E.;Proc. Amer. Math. Soc.,1971

2. The minimum modulus of a polynomial on the unit circle;Clunie, J.;Quart. J. Math. Oxford Ser. (2),1959

Cited by 3 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Zero-free neighborhoods around the unit circle for Kac polynomials;Periodica Mathematica Hungarica;2021-08-07

2. Beam-forming applications of polynomials with restricted coefficients;Electromagnetic Modelling and Measurements for Analysis and Synthesis Problems;1991

3. On the Maximum Modulus for a Certain Class of Unimodular Trigonometric Polynomials;Recent Advances in Fourier Analysis and Its Applications;1990

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