The asymptotic distribution function of the 4-dimensional shifted van der corput sequence

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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).

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Tatra Mountains Mathematical Publications

The Journal of Slovak Academy of Sciences

Journal Information


CiteScore 2017: 0.37

SCImago Journal Rank (SJR) 2017: 0.363
Source Normalized Impact per Paper (SNIP) 2017: 0.482

Mathematical Citation Quotient (MCQ) 2017: 0.14

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