\begin{definition}[Definition:Dirichlet Series]
Let $a_n: \N \to \C$ be an arithmetic function.
Its '''Dirichlet series''' is a complex function $f: \C \to \C$ defined by a series:
:$\ds \map f s = \sum_{n \mathop = 1}^\infty a_n n^{-s}$
which is defined at the points where it converges.
\end{definition}