Distribution of points on the circle

[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.

[发布日期] 2007-11-01

[关键词] unit circle;complex numbers;distribution;arcs