# Wolfgang Steiner: The local discrepancy of generalized van der Corput sequences

## This is a joint work with Klaus Scheicher.

Let be a real number and

be the set of all (inversed) greedy expansions in base . Then the -th element of the generalised van der Corput sequence in base is defined by the -th element of with respect to the lexicographical order, . If the expansion of 1 in base is finite or ultimately periodic, then we have a substitution such that the digits of are the lengths of the words in the expansion of with respect to this substitution. This allows us to get explicit formulae for the local discrepancy ( ) of the sequence. If is a Pisot number and the -polynomial is the minimal polynomial of , then the local discrepancy is bounded (in ) if and only if either the -expansion of is finite or its tail is the same as the tail of the expansion of 1.