## 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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### References:

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