# Definition:Arithmetic Function

## Definition

An arithmetic function or arithmetical function is a complex valued function defined on the strictly positive integers.

That is, a mapping:

$f: \Z_{>0} \to \C$

## Linguistic Note

In the context of an arithmetic function, the word arithmetic is pronounced with the stress on the first and third syllables: a-rith-me-tic, rather than on the second syllable: a-rith-me-tic.

This is because the word is being used in its adjectival form.