Cyclic shifts of the van der Corput set

Bilyk, Dmitriy

doi:10.1090/S0002-9939-09-09854-2

Cyclic shifts of the van der Corput set
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Proc. Amer. Math. Soc. 137 (2009), 2591-2600 Request permission

Abstract:

In 1980, 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. In the present paper, we construct a specific example of such a shift.

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