On Some Power Sum Problems of Montgomery and Turan

被引：3

作者：

Andersson, Johan ^{[1
]}

机构：

[1] Stockholm Univ, Dept Math, SE-10691 Stockholm, Sweden

来源：

INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2008年 / 2008卷

关键词：

D O I：

10.1093/imrn/rnn015

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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(vertical bar zk vertical bar=1) max(nu=1,...,n)(h) vertical bar Sigma(n)(k=1) Z(k)(nu)vertical bar <= (h - 1 + o(1)root 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 root logn.

引用

页数：9

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