Bloch's Theorem (complex Variables) - Valiron's Theorem

Valiron's Theorem

Bloch's theorem was inspired by the following theorem of Georges Valiron:

Theorem. If f is a non-constant entire function then there exist discs D of arbitrarily large radius and analytic functions φ in D such that f(φ(z)) = z for z in D.

Bloch's theorem corresponds to Valiron's theorem via the so-called Bloch's Principle.