An extremal problem for the geometric mean of polynomials

E. Beller; D. J. Newman

doi:10.1090/S0002-9939-1973-0316686-X

An extremal problem for the geometric mean of polynomials

E. Beller
, D. J. Newman

Department of Mathematics

Yeshiva University

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

Abstract

Let M_{0, n} be the maximum of the geometric mean of all nth degree polynomials (equation omited) which satisfy |a_k| = l, k=0, 1, …, n. We show the existence of certain polynomials R_n whose geometric mean is asymptotic to √n, thus proving that M_{0, n} is itself asymptotic to √n.

Original language	English
Pages (from-to)	313-317
Number of pages	5
Journal	Proceedings of the American Mathematical Society
Volume	39
Issue number	2
DOIs	https://doi.org/10.1090/S0002-9939-1973-0316686-X
State	Published - Jul 1973

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abstract = "Let M0, n be the maximum of the geometric mean of all nth degree polynomials (equation omited) which satisfy |ak| = l, k=0, 1, …, n. We show the existence of certain polynomials Rn whose geometric mean is asymptotic to √n, thus proving that M0, n is itself asymptotic to √n.",

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AB - Let M0, n be the maximum of the geometric mean of all nth degree polynomials (equation omited) which satisfy |ak| = l, k=0, 1, …, n. We show the existence of certain polynomials Rn whose geometric mean is asymptotic to √n, thus proving that M0, n is itself asymptotic to √n.

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An extremal problem for the geometric mean of polynomials

Abstract

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