An Asymptotic Distribution Function of the Three-Dimensional Shifted van der Corput Sequence

Abstract

In this paper, we apply the Weyl's limit relation to calculate the limit , where γ q ( n ) is the van der Corput sequence in base q, g ( x , y , z), is the asymptotic distribution function of ( γ q ( n ), γ q ( n + 1 ), γ q ( n + 2 )), and F ( x , y , z) = max ( x , y , z ), min ( x , y , z), and xy z, respectively.