Distribution Properties ofG-Additive Functions Original Research Article

We extend previous results of Delange (Acta Arith.21, 1972, 285–298) concerning the existence of distribution functions of certainq-adic digital functions to the case of digital expansions with respect to linear recurrences with decreasing coefficients. Furthermore we investigate a special case of digital functions and give a functional equation for the related distribution function. We prove uniqueness and continuity of the solution of this equation.