Quotients of arithmetical functions under the Dirichlet convolution
Quotients of arithmetical functions under the Dirichlet convolution
We study existence of a solution of the arithmetical equation $f\ast h = g$ in $f,$ where $f\ast h$ is the Dirichlet convolution of arithmetical functions $f$ and $h,$ and derive an explicit expression for the solution. As applications we obtain expressions for the Möbius function $\mu$ and the so-called …