Category:Definitions/Multiplicative Functions

This category contains definitions related to Multiplicative Functions.
Related results can be found in Category:Multiplicative Functions.

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

Then $f$ is multiplicative if and only if:

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

where $m \perp n$ denotes that $m$ is coprime to $n$.