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Regularities of the distribution of abstract van der Corput sequences

Author(s): Wolfgang Steiner

Journal: Uniform Distribution Theory
ISSN 1336-913X

Volume: 4;
Issue: 2;
Start page: 81;
Date: 2009;
Keywords: Local discrepancy | bounded remainder set | numeration system | automaton | Pisot number | $beta$-transformation | van der Corput sequence | abstract numeration system
Similarly to $\beta$-adic van der Corput sequences, abstract van der Corput sequences can be defined by abstract numeration systems. Under some assumptions, these sequences are low discrepancy sequences. The discrepancy function is computed explicitly, and the bounded remainder sets of the form $[0,y)$ are characterized.