Distribution of the values of a sum of additive functions with shifted arguments
A necessary and sufficient condition is found for a couple of additive functions \(g_ 1\), \(g_ 2\) to have the property that \(g_ 1(n)+ g_ 2(n+1)\) has a limiting distribution with a suitable centering. This extends a result of \textit{A. Hildebrand} [Trans. Am. Math. Soc. 310, 257- 276 (1988; Zbl 0707.11057)], where \(g(n+1)- g(n)\) is considered. The condition is equivalent to saying that the functions themselves have limiting distributions under suitable centering.
scientific article; zbMATH DE number 578699
scientific article