Cyclic shifts of the van der Corput set

2008/11/12 by Dmitriy Bilyk, Bilyk, Dmitriy
Mathematics · #11K38 (Primary) #42B05 (Secondary) #FOS: Mathematics #Functional Analysis (math.FA) #Number Theory (math.NT) #math.FA #math.NT #msc:11K38 #msc:42B05

paper · pdf · doi:10.48550/arxiv.0811.1871

12 pages

arxiv created 2008/11/12 · arxiv updated 2009/12/01

Abstract

In [13], K. Roth showed that the expected value of the L² discrepancy of the cyclic shifts of the N point van der Corput set is bounded by a constant multiple of √(log N), thus guaranteeing the existence of a shift with asymptotically minimal L² discrepancy, [11]. In the present paper, we construct a specific example of such a shift.

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