Lemma 3.7 (Landau). Assuming that:

$z_{0} \in ℂ$ and $r > 0$
$f$ analytic in $B (z_{0}, r)$
for some $M > 1$ we have $| f (z) | < e^{M} | f (z_{0}) |$ for all $z \in B (z_{0}, r)$

Then for

z \in B (z_{0}, r ∕ 4)

| \frac{f^{'} (z)}{f (z)} - \sum_{ρ \in Z} \frac{1}{z - ρ} | \leq \frac{96 M}{r},

where $Z$ is the set of zeroes of $f$ in $\bar{B (z_{0}, r ∕ 2)}$ , counted with multiplicities.