Average growth-behavior and distribution properties of generalized weighted digit-block-\-counting functions
The authors study a generalization of several digit functions in form of a block-counting function depending on a sequence of real weights. In particular this generalizes the classical sum-of-digits function. They derive a formula for the first order moments of these functions and use this result in order to establish a Delange type result for these moments in the instance where the weight sequence converges. In the second part of the paper distribution properties of generalized weighted digit-block-counting sequences are studied, in particular a necessary and sufficient condition is presented under which such sequences are uniformly distributed modulo one.
scientific article; zbMATH DE number 5313117