On some power sum problems of Montgomery and Turan

Johan Andersson

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arXiv · 0706.4131

On some power sum problems of Montgomery and Turan

Johan Andersson

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Abstract

We use an estimate for character sums over finite fields of Katz to solve open problems of Montgomery and Turan. Let h=>2 be an integer. We prove that inf_{|z_k| => 1} max_{v=1,...,n^h} |sum_{k=1}^n z_k^v| <= (h-1+o(1)) sqrt n. This gives the right order of magnitude for the quantity and improves on a bound of Erdos-Renyi by a factor of the order sqrt log n.

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BibTeX RIS

Johan Andersson. 2007-07-11. On some power sum problems of Montgomery and Turan. https://arxiv.org/abs/0706.4131

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