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