Use this tag for questions related to Dirichlet convolution in number theory

Dirichlet convolution is a type of convolution used in number theory for arithmetic functions. It forms a commutative ring under pointwise addition. It is defined as

\begin{equation*} (f\ast g)(n)=\sum_{d|n}f(d)g(\frac{n}{d}) \end{equation*}

where $f$ and $g$ are two arithmetic functions, and $d$ is a divisor of $n.$

Note that the multiplication of Dirichlet series is compatible with Dirichlet convolution.