EXTENSIONS OF THE CLASS OF MULTIPLICATIVE FUNCTIONS

Pentti Haukkanen

Pentti Haukkanen

Keywords: quasimultiplicativefunction, semimultiplicativefunction, Selberg multiplicative function, Ramanujan’s sum, regular integer

Abstract

We consider the classes of quasimultiplicative, semimultiplicative and Selberg multiplicative functions as extensions of the class of multiplicative functions. We apply these concepts to Ramanujan’s sum and its analogue with respect to regular integers (mod r).