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Distribution of points on the circle

Authors
Journal
Journal of Number Theory
0022-314X
Publisher
Elsevier
Publication Date
Volume
127
Issue
1
Identifiers
DOI: 10.1016/j.jnt.2007.01.009
Keywords
  • Unit Circle
  • Complex Numbers
  • Distribution
  • Arcs

Abstract

Abstract In connection with the proof of his celebrated “2.4-Theorem”, Freiman proved that if α 1 , … , α N are real numbers such that each interval [ u , u + 1 / 2 ) contains at most n of the α j mod 1, then | ∑ j = 1 N exp ( 2 π i α j ) | ⩽ 2 n − N . Freiman's result was extended by Moran and Pollington, and recently by Lev. This paper contains further extensions.

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