On some power sum problems of Montgomery and Turan
Number Theory
2007-07-11 v3
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.
Cite
@article{arxiv.0706.4131,
title = {On some power sum problems of Montgomery and Turan},
author = {Johan Andersson},
journal= {arXiv preprint arXiv:0706.4131},
year = {2007}
}