Affiliation:
1. Technische Universität Wien , Wien , Austria
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.
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