Regularities of the distribution of abstract van der Corput sequences

Wolfgang Steiner (1)

1 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications

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.

Domaines: Théorie des nombres [math.NT]; Mathématique discrète [cs.DM]

Wolfgang Steiner. Regularities of the distribution of abstract van der Corput sequences. Uniform Distribution Theory, 2009, 4 (2), pp.81-100. ⟨hal-00323846v2⟩