Distribution of Multiplicative Functions Defined on Semigroups

Abstract

The value distribution problem for real-valued multiplicative functions defined on an additive arithmetical semigroup is examined. We prove that, in contrast to the classical theory of number-theoretic functions defined on the semigroup of natural numbers, this problem is equivalent to that for additive functions we derive general sufficient conditions for the existence of a limit law for appropriately normalized multiplicative functions. Quaestiones Mathematicae 24(3) 2001, 335-34