On the distribution of translates of additive functions (Q1314843)

The authors' aim is to describe those additive functions \(f\) for which \(P(E)f\) has a limiting distribution under a suitable centering; here \(P\) is a polynomial and \(E\) denotes the difference operator. This is achieved if \(P(1)\neq 0\), or if \(P'(1)\neq 0\) and the centering vanishes, and a weaker result is proved in the case \(P(1)= P'(1)=0\). Also a condition is given for \(g(n+1)- f(n)\) to have a limiting distribution, where \(f\), \(g\) are both additive functions.