# When are entire functions surjective?

Is there some useful criterion to determine whether or not an entire function is surjective?

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Indeed. And it is surjective if and only if it not of the form $e^{h(z)}+\alpha$ for a suitable constant $\alpha$ and a suitable entire function $h(z)$. –  Roland Bacher Jun 3 '10 at 10:13
But certainly if there is no $\alpha \in \mathbb{C}$ such that $\frac{f'(z)}{f(z) - \alpha}$ is entire, we can conclude that $f$ is not surjective. –  Saul Glasman Jun 3 '10 at 20:59