Definition:Formal Product of Dirichlet Series

Definition
Let $f,g : \N \to \C$ be arithmetic functions.

Let $F,G$ be their formal Dirichlet series.

The formal product of $F$ and $G$ is the formal Dirichlet series:
 * $\displaystyle \sum_{n \mathop = 1}^\infty \frac{(f*g)(n)}{n^s}$

where $*$ denotes Dirichlet convolution.

Also see

 * Dirichlet Series of Convolution of Arithmetic Functions
 * Definition:Ring of Arithmetic Functions