Discrepancy estimates for index-transformed uniformly distributed sequences

2014/07/31 by Peter Kritzer, Kritzer, Peter, Gerhard Larcher +3
Computer Science · Mathematics · #Coding theory and cryptography #Mathematical Approximation and Integration #math.NT #msc:11K06 #msc:11K31 #msc:11K36 #msc:11K38

paper · pdf · doi:10.48550/arxiv.1407.8287

arxiv created 2014/07/31 · arxiv updated 2014/08/01

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^α\rfloor with 0 < α< 1.

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