ABSTRACT
When we consider the domain of an arithmetic function as ℤ+, the set of positive integers, we could prove that the set ℳ of multiplicative functions is a subgroup of the group of units in the ring ( A https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315139463/240bbb93-6815-40d4-a336-935ccad8ea72/content/eq1539.tif"/> ,+,·) (see Chapter I). However, the zero function trivially satisfies the conditions for multiplicativity: namely () f ( m ) f ( n ) = f ( mn ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315139463/240bbb93-6815-40d4-a336-935ccad8ea72/content/eq1540.tif"/>
