Definition:Additive Arithmetic Function

This page is about Additive Arithmetic Function. For other uses, see Additive Function.

Definition

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

Then $f$ is additive if and only if:

$m \perp n \implies \map f {m n} = \map f m + \map f n$

Also see

• Definition:Completely Additive Function

• Definition:Multiplicative Arithmetic Function
• Definition:Completely Multiplicative Function

• Results about additive arithmetic functions can be found here.