The distribution of generalized sum-of-digits functions in residue classes
A function \(f:\mathbb{N}\to\mathbb{Z}\) has limit distribution modulo \(m\) if the limit \[ \lim_{N\to\infty} \tfrac{1}{N} \#\{0\leq n< N: f(n)\equiv k\bmod m\} \] exists for each integer \(k\); it is called uniform if this limit is always \(\frac{1}{m}\). The author proves a necessary and sufficient criterion for uniform distribution modulo \(m\) in the case, that \(m\) is prime and the function \(f\) is \(Q\)-additive with respect to a base-\(Q\) representation in a general numeration system. This generalizes a known result of the sum-of-digit function.
scientific article; zbMATH DE number 1420251