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:

$\ds \sum_{n \mathop = 1}^\infty \frac {\map {\paren {f * g} } n} {n^s}$

where $*$ denotes Dirichlet convolution.

Also see

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