Cyclic shifts of the van der Corput set

Details Cyclic shifts of the van der Corput set Cyclic shifts of the van der Corput set

2008-11-12

arxiv.org/abs/0811.1871v1

Mathematics

Number Theory

12 pages

Scientific paper

In [13], K. Roth showed that the expected value of the $L^2$ discrepancy of
the cyclic shifts of the $N$ point van der Corput set is bounded by a constant
multiple of $\sqrt{\log N}$, thus guaranteeing the existence of a shift with
asymptotically minimal $L^2$ discrepancy, [11]. In the present paper, we
construct a specific example of such a shift.

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