%0 Journal Article
%T Regularities of the distribution of abstract van der Corput sequences
%A Wolfgang Steiner
%J Uniform Distribution Theory
%D 2009
%I Mathematical Institute of the Slovak Academy of Sciences
%X 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.
%K Local discrepancy
%K bounded remainder set
%K numeration system
%K automaton
%K Pisot number
%K $ beta$-transformation
%K van der Corput sequence
%K abstract numeration system
%U http://www.boku.ac.at/MATH/udt/vol04/no2/5Steiner09-2.pdf