The minimum modulus of polynomials
HTML articles powered by AMS MathViewer
- by E. Beller and D. J. Newman PDF
- Proc. Amer. Math. Soc. 45 (1974), 463-465 Request permission
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 $|P(z)| > C\sqrt n$ for all $z$ on $|z| = 1$ ($C$ is a positive absolute constant).References
- E. Beller and D. J. Newman, An $l_{1}$ extremal problem for polynomials, Proc. Amer. Math. Soc. 29 (1971), 474–481. MR 280688, DOI 10.1090/S0002-9939-1971-0280688-0
- J. Clunie, The minimum modulus of a polynomial on the unit circle, Quart. J. Math. Oxford Ser. (2) 10 (1959), 95–98. MR 106271, DOI 10.1093/qmath/10.1.95
- J. E. Littlewood, Lectures on the Theory of Functions, Oxford University Press, 1944. MR 0012121
- E. C. Titchmarsh, The Theory of the Riemann Zeta-Function, Oxford, at the Clarendon Press, 1951. MR 0046485
Additional Information
- © Copyright 1974 American Mathematical Society
- 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