\begin{definition}[Definition:Dirichlet Inverse of Arithmetic Function]
Let $f : \N \to \C$ be an arithmetic function.
Let $\varepsilon$ be the identity arithmetic function.
A '''Dirichlet inverse''' of $f$ is an arithmetic function $g$ such that $g*f = \varepsilon$, where $*$ denotes Dirichlet convolution.
That is, an inverse of $f$ in the ring of arithmetic functions.
\end{definition}