Gaussian asymptotic properties of the sum-of-digits function (Q676278)

The authors consider digital expansions with respect to linear recurrences. They show that the sum-of-digits function has an asymptotic Gaussian behaviour. The authors actually prove the Gaussian law in the more general framework of numeration systems associated with a primitive substitution on a finite alphabet. The proof is based on a central limit theorem of Statulevičius and large deviation arguments. Furthermore some new summation formulae are established. This paper complements earlier results of the authors as well as a summation formulae due to \textit{P. J. Grabner} and \textit{R. F. Tichy} [Manuscr. Math. 70, 311-324 (1991; Zbl 0725.11005)].