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Precise distribution properties of the van der Corput sequence and related sequences. (English) Zbl 1088.11060

The authors study the \(L_p\)-discrepancies of the van der Corput sequence and certain more general digital \((0,1)\)-sequences. They show, that within this class the van der Corput sequence is the worst distributed one with respect to \(L_2\)-discrepancy. Furthermore, it is shown that the \(L_p\)-discrepancies of the van der Corput sequence satisfy a central limit theorem. The proofs depend on precise calculations of digital sums and Walsh series expansions.

MSC:

11K38 Irregularities of distribution, discrepancy
11K06 General theory of distribution modulo \(1\)
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