# 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}
}
• Published 1 June 2000
• Mathematics
• Journal of Number Theory
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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## References

SHOWING 1-10 OF 18 REFERENCES
Uniform dilations
• 1992
Every sufficiently large finite setX in [0,1) has a dilationnX mod 1 with small maximal gap and even small discrepancy. We establish a sharp quantitative version of this principle, which puts into a
Combinatorial complexity bounds for arrangements of curves and spheres
• Mathematics, Computer Science
Discret. Comput. Geom.
• 1990
Upper and lower bounds for extremal problems defined for arrangements of lines, circles, spheres, and alike are presented and it is proved that the maximum number of edges boundingm cells in an arrangement ofn lines is Θ(m2/3n 2/3 +n), and that it isO(m3/2β(m) forn unit-circles.
Non-averaging Subsets and Non-vanishing Transversals
• Computer Science, Mathematics
J. Comb. Theory, Ser. A
• 1999
It is shown that every set ofintegers contains a subset of size?(n1/6) in which no element is the average of two or more others, and it is proved that for every?>0 and everym>m(?) the following holds.
Topics in Multiplicative Number Theory
Three basic principles.- The large sieve.- Arithmetic formulations of the large sieve.- A weighted sieve and its application.- A lower bound of Roth.- Classical mean value theorems.- New mean value
Combinatorial geometry
• Mathematics, Computer Science
Wiley-Interscience series in discrete mathematics and optimization
• 1995
\indent This beautiful discipline emerged from number theory after the fruitful observation made by Minkowski (1896) that many important results in diophantine approximation (and in some other
Ten lectures on the interface between harmonic analysis and analytic number theory. CBMS Regional conference series in mathematics #84
• Ten lectures on the interface between harmonic analysis and analytic number theory. CBMS Regional conference series in mathematics #84
• 1994
Newman Polynomials on |z| = 1
• Ind. Univ. Math. J
• 1983