Regularities of the distribution of abstract van der Corput sequences

Mathematics – Number Theory

Scientific paper

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Scientific paper

Similarly to $\beta$-adic van der Corput sequences, abstract van der Corput
sequences can be defined for abstract numeration systems. Under some
assumptions, these sequences are low discrepancy sequences. The discrepancy
function is computed explicitely, and a characterization of bounded remainder
sets of the form $[0,y)$ is provided.

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