Abstract
For any \({G(k) \uparrow \infty}\) , there exists a sequence {n k } of integers with 1 ≤ n k+1 − n k ≤ G(k) such that the discrepancies of {n k x} obey the law of the iterated logarithm in the same way as uniform distributed i.i.d.
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Communicated by J. Schoißengeier.
The author was supported in part by KAKENHI 19204008.
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Fukuyama, K. A metric discrepancy result for a lacunary sequence with small gaps. Monatsh Math 162, 277–288 (2011). https://doi.org/10.1007/s00605-009-0185-0
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DOI: https://doi.org/10.1007/s00605-009-0185-0