One-sided power sum and cosine inequalities

F. Beukers; R. Tijdeman

doi:10.1016/j.indag.2012.11.009

One-sided power sum and cosine inequalities

F. Beukers, R. Tijdeman

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Abstract

In this note we prove results of the following types. Let be given distinct complex numbers satisfying the conditions for and for every there exists an such that . Then If, moreover, none of the ratios with is a root of unity, then The constant −1 in the former result is the best possible. The above results are special cases of upper bounds for obtained in this paper.

Original language	English
Pages (from-to)	373-381
Number of pages	9
Journal	Indagationes Mathematicae
Volume	24
Issue number	2
DOIs	https://doi.org/10.1016/j.indag.2012.11.009
Publication status	Published - Mar 2013

Keywords

Power sums
One-sided inequality
Sums of cosines
Littlewood conjecture
Multistep methods

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abstract = "In this note we prove results of the following types. Let be given distinct complex numbers satisfying the conditions for and for every there exists an such that . Then If, moreover, none of the ratios with is a root of unity, then The constant −1 in the former result is the best possible. The above results are special cases of upper bounds for obtained in this paper.",

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AB - In this note we prove results of the following types. Let be given distinct complex numbers satisfying the conditions for and for every there exists an such that . Then If, moreover, none of the ratios with is a root of unity, then The constant −1 in the former result is the best possible. The above results are special cases of upper bounds for obtained in this paper.

KW - Power sums

KW - One-sided inequality

KW - Sums of cosines

KW - Littlewood conjecture

KW - Multistep methods

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DO - 10.1016/j.indag.2012.11.009

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VL - 24

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JO - Indagationes Mathematicae

JF - Indagationes Mathematicae

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One-sided power sum and cosine inequalities

Abstract

Keywords

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