Definition:Arithmetic Function

Definition

An arithmetic function or arithmetical function is a complex valued function defined on the natural numbers.

That is, a function:

$f: \N \to \C$

Examples

Common examples of arithmetic functions include:

• The Möbius function $\mu(n)$

• The Euler phi function $\phi(n)$

• The von Mangoldt function $\Lambda(n)$

See Also

Dirichlet series

Linguistic Note

In this context, 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.