Block additive functions on the Gaussian integers

Michael M. Drmota (1) , Peter Grabner (2) , Pierre Liardet (3)

1 TU Wien - Vienna University of Technology = Technische Universität Wien
2 institut für Analysis und Computational Number Theory
3 LATP - Laboratoire d'Analyse, Topologie, Probabilités

We present three conceptually different methods to prove distribution results for block additive functions with respect to radix expansions of the Gaussian integers. Based on generating function approaches we obtain a central limit theorem and asymptotic expansions for the moments. Furthermore, these generating functions as well as ergodic skew products are used to prove uniform distribution in residue classes and modulo 1.

Mots clés: digital sequence; block function; numeration; Gauss integer

Domaines: Théorie des nombres [math.NT]

Michael M. Drmota, Peter Grabner, Pierre Liardet. Block additive functions on the Gaussian integers. Acta Arithmetica, 2008, 135 (4), pp.299--332. ⟨10.4064/aa135-4-1⟩. ⟨hal-00871045⟩