Definition:Multiplicative Arithmetic Function

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


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 $n$.

That is, a multiplicative function is one where the value of a product of two coprime numbers equals the product of the value of each one individually.

Also see

  • Results about multiplicative functions can be found here.