On Uniformly Distributed Dilates of Finite Integer Sequences

@article{Konyagin2000OnUD,
  title={On Uniformly Distributed Dilates of Finite Integer Sequences},
  author={Sergei Konyagin and Imre Z. Ruzsa and Wilhelm Schlag},
  journal={Journal of Number Theory},
  year={2000},
  volume={82},
  pages={165-187}
}
Given N nonzero real numbers a1<…<aN, we consider the problem of finding a real number α so that αa1, …, αaN are close to be uniformly distributed modulo one (this question is attributed to Komlos). First, it turns out that it suffices to consider integers a1, …, aN. Given various quantities that measure how close a sequence is to being uniformly distributed, e.g., the size of the largest gap between consecutive points on the circle, discrepancy, or the number of points falling into any… 
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