Resumen de Regularities of the Distribution of ß-adic van der Corput Sequences

Wolfgang Steiner

• For Pisot numbers ß with irreducible ß-polynomial, we prove that the discrepancy function D(N, [0,y)) of the ß-adic van der Corput sequence is bounded if and only if the ß-expansion of y is finite or its tail is the same as that of the expansion of 1. If ß is a Parry number, then we can show that the discrepancy function is unbounded for all intervals of length . We give explicit formulae for the discrepancy function in terms of lengths of iterates of a reverse ß-substitution.