Let $f$ be an arithmetic function. We define, for all real $s$ such that the series converges,
$$L_f(s) = \sum_{k=1}^{\infty} \frac{f(k)}{k^s}$$
The abscissa of convergence of $L_f$ is defined as
$$A_c(f) = \inf\left\{s \in \mathbb{R} \mid \text{the series } \sum \frac{f(k)}{k^s} \text{ converges absolutely}\right\}.$$
Show that if $s > A_c(f)$, then the series $\sum \frac{f(k)}{k^s}$ converges absolutely.