Definition:Multiplicative Arithmetic Function

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This page is about multiplicative functions in number theory. For other uses, see Definition:Multiplicative Function.

Definition

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


Then $f$ is multiplicative if and only if:

$m \perp n \implies f \left({m n}\right) = f \left({m}\right) f \left({n}\right)$

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.


Sources