Abstract
In this paper we show discrepancy bounds for index-transformed uniformly distributed sequences. From a general result we deduce very tight lower and upper bounds on the discrepancy of index-transformed van der Corput-, Halton-, and $(t,s)$-sequences indexed by the sum-of-digits function. We also analyze the discrepancy of sequences indexed by other functions, such as, e.g., $\lfloor n^{\alpha}\rfloor$ with $0 < \alpha < 1$.
Citation
Peter Kritzer. Gerhard Larcher. Friedrich Pillichshammer. "Discrepancy estimates for index-transformed uniformly distributed sequences." Funct. Approx. Comment. Math. 51 (1) 197 - 220, September 2014. https://doi.org/10.7169/facm/2014.51.1.12
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