The distribution of real-valued \(Q\)-additive functions modulo 1
A mixed radix system \(Q=\{Q_j\}_{j\geq 0}\) is a sequence of strictly increasing positive integers \(Q_j\) with \(Q_0=1\) such that \(Q_j|Q_{j+1}\) for all \(j\). Then each non-negative integer \(n\) has a unique representation \(n=\sum_{j\geq 0}a_j(n)Q_j\), and a \(Q\)-additive function is of the form \(f(n)=\sum_{j\geq 0}f_j(a_j(n))\) where \(f_j(0)=0\). A simple example of a \(Q\)-additive function is the sum-of-digits function. The author investigates conditions under which the sequence \((f(n))\) has a limit distribution mod 1. In order to prove this result, the author considers so-called \(Q\)-multiplicative functions and establishes mean value theorems for these.
scientific article; zbMATH DE number 1709877