PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.) Vol. 71(85), pp. 2739 (2002) 

ON SUMMATORY FUNCTIONS OF ADDITIVE FUNCTIONS AND REGULAR VARIATIONAleksandar Ivi\'cKatedra Matematike RGFa, Univerziteta u Beogradu, Dju\v sina 7, 11000 Beograd, Serbia (Yugoslavia)Abstract: 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 regular variation. Some new Abelian and Tauberian results for additive functions of the form $F(n)=\sum\limits_{p^\alphan}\alpha h(p)$ are obtained. Keywords: Regularly and slowly varying functions; arithmetic sums; additive functions; Abelian and Tauberian theorems Classification (MSC2000): 11N37; 26A12 Full text of the article:
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