Van der corput’s difference theorem - Israel Journal of Mathematics

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ID: 267785
1970
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Abstract
We obtain a sufficient condition for a subsetH of positive integers to satisfy that the equidistribution (mod 1) of the sequences (u n+h − u n; n=1, 2, ···) for allh ∈H implies the equidistribution of (u n). Our condition is satisfied, for example, for the following sets: (1)H={n − m; n ∈ I, m ∈ I, n>m}, whereI is any infinite subset of integers; (2)H={| ψ (n)|; ψ(n)≠0,n ∈ Z}, where ψ is a nonconstant polynomial with integral coefficients having at least one integral zero (modq) for allq=2, 3, ···; (3)H={p+1;p is a prime} andH={p − 1;p is a prime}.
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kamae1970israelvan Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors T. Kamae;M. Mendes France;T. Kamae;M. Mendes France;
Journal israel journal of mathematics
Year 1970
DOI
doi:10.1007/BF02761498
URL
https://doi.org/10.1007/bf02761498
Keywords
analysis mathematics general theoretical applications of mathematics mathematical and computational physics algebra group theory and generalizations

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