Integral limit theorems for sums of additive functions with shifted arguments

摘要

In this paper we find necessary and sufficient conditions for the vanishing of, the limit distribution for a linear combination of two real-valued additive functions. We obtain results for g1(an+b)/B1(x)+g)cn+d)/B2(x)-A(x), where a > 0,b,c > 0, and d are integers with ad - be #0, that are almost as strong as in the case of a single additive function. As an .application, we resolve a conjecture of Katai.