Abstract
Let (n k ) k ≥ 1 be a lacunary sequence of integers, satisfying certain number-theoretic conditions. We determine the limit distribution of \({\sqrt{N} D_N (n_{k} x)}\) as \({N \to \infty}\) , where D N (n k x) denotes the discrepancy of the sequence (n k x) k ≥ 1 mod 1.
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Communicated by J. Schoißengeier.
C. Aistleitner’s research supported by FWF grant S9603-N23.
I. Berkes’s research supported by FWF grant S9603-N23 and OTKA grant K 67961.
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Aistleitner, C., Berkes, I. Limit distributions in metric discrepancy theory. Monatsh Math 169, 253–265 (2013). https://doi.org/10.1007/s00605-012-0378-9
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DOI: https://doi.org/10.1007/s00605-012-0378-9