The asymptotic distribution function of the 4-dimensional shifted van der corput sequence
Vladimír Baláž, Jana Fialová, Markus Hofer, Maria Rita Iacò, Oto Strauch · Tatra Mountains Mathematical Publications · 2015
Abstract Let γq(n) be the van der Corput sequence in the base q and g(x, y, z, u) be an asymptotic distribution function of the 4-dimensional sequence In this paper we find an explicit formula for g(x, x, x, x) and then as an example we find the limit for the base q = 4, 5, 6, . . . Also we find an explicit form of sth iteration T(s)(x) of the von Neumann-Kakutani transformation defined by T(γq(n)) = γq(n + 1).