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An overview of results and problems concerning the asymptotic behaviour for summatory functions of a certain class of additive functions is given. The class of functions in question involves Karamata's regular variation. Some new Abelian and Tauberian results for additive functions of the form F(n) = ∑_p^α||nα h(p) are given.arXiv:math/0311345v1 fatcat:ljdhrpswabfjrpfkvdvi4fwy3m