Let $f$ and $g$ be two arithmetic functions with finite abscissas of convergence. Show that, for all $s > \max\left(A_c(f), A_c(g)\right)$, $$L_{f*g}(s) = L_f(s) L_g(s)$$
Let $f$ and $g$ be two arithmetic functions with finite abscissas of convergence. Show that, for all $s > \max\left(A_c(f), A_c(g)\right)$,
$$L_{f*g}(s) = L_f(s) L_g(s)$$