N T ] 2 0 N ov 2 00 3 ON SUMMATORY FUNCTIONS OF ADDITIVE FUNCTIONS AND REGULAR VARIATION

We shall denote the set of all regularly varying functions by R. We shall also denote by L the set of slowly slowly varying (or slowly oscillating) functions, namely those functions in R for which the index ρ = 0. It is easy to show that if h ∈ R, then there exists L ∈ L such that h(x) = xL(x), with ρ being the index of h. Slowly varying functions arise… CONTINUE READING