Discrepancy results for the Van der Corput sequence

2017/10/04 by Spiegelhofer, Lukas
#11A63 (Primary) #11K31 (Secondary) #11K38 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1710.01560

Abstract

Let d_N=ND_N(ω) be the discrepancy of the Van der Corput sequence in base 2. We improve on the known bounds for the number of indices N such that d_N≤ log N/100. Moreover, we show that the summatory function of d_N satisfies an exact formula involving a 1-periodic, continuous function. Finally, we show that d_N is invariant under digit reversal in base 2.

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