Distribution of points on the circle

JOURNAL OF NUMBER THEORY

卷:127

Article

Rodseth, Oystein J.

关键词: unit circle;    complex numbers;    distribution;    arcs;   

DOI  :  10.1016/j.jnt.2007.01.009

来源: Elsevier

【 摘 要 】

In connection with the proof of his celebrated 2.4-Theorem, Freiman proved that if alpha(l),...,alpha(N) are real numbers such that each interval [u, u + 1/2] contains at most n of the alpha(j) mod 1, then vertical bar Sigma(N)(j=1) exp(2 pi i alpha(j))vertical bar <= 2n-N. Freiman's result was extended by Moran and Pollington, and recently by Lev. This paper contains further extensions. (C) 2007 Elsevier Inc. All rights reserved.

【 授权许可】

Free