Definition:Additive Arithmetic Function

Definition
Let $f : \N \to \C$ be an arithmetic function.

Then $f$ is additive :
 * $m \perp n \implies \map f {m n} = \map f m + \map f n$

Also see

 * Definition:Completely Additive Function


 * Definition:Multiplicative Arithmetic Function
 * Definition:Completely Multiplicative Function