Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4673096 | Indagationes Mathematicae | 2013 | 9 Pages |
Abstract
In this note we prove results of the following types. Let be given distinct complex numbers zjzj satisfying the conditions |zj|=1,zj≠1|zj|=1,zj≠1 for j=1,…,nj=1,…,n and for every zjzj there exists an ii such that zi=zj¯. Then infk∑j=1nzjk≤−1. If, moreover, none of the ratios zi/zjzi/zj with i≠ji≠j is a root of unity, then infk∑j=1nzjk≤−1π4logn. The constant −1 in the former result is the best possible. The above results are special cases of upper bounds for infk∑j=1nbjzjk obtained in this paper.
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Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Frits Beukers, Rob Tijdeman,