Discrepancy Results for The Van Der Corput Sequence

Abstract

Abstract Let dN = NDN (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 dN ≤ log N/100. Moreover, we show that the summatory function of dN satisfies an exact formula involving a 1-periodic, continuous function. Finally, we give a new proof of the fact that dN is invariant under digit reversal in base 2.