Definition:Arithmetic Function

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

That is, a mapping:

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

Also see

  • Results about arithmetic functions can be found here.


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.