Dirichlet series inversion

Dirichlet series inversion is a method in analytic number theory that relates Dirichlet series and arithmetic functions. A Dirichlet series is a series of the form \[ F(s) = \sum_{n=1}^\infty \frac{a(n)}{n^s} \] where \( a(n) \) represents a sequence of complex numbers and \( s \) is a complex variable.