PlanetMath: little Picard theorem

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little Picard theorem

(Theorem)

The range of a nonconstant entire function is either the whole complex plane $\mathbb{C}$ , or the complex plane with a single point removed. In other words, if an entire function omits two or more values, then it is a constant function.

"little Picard theorem" is owned by Koro.

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Cross-references: constant function, point, complex plane, entire function, range
There are 2 references to this entry.

This is version 2 of little Picard theorem, born on 2002-12-11, modified 2003-11-13.
Object id is 3734, canonical name is LittlePicardTheorem.
Accessed 3019 times total.

Classification:

AMS MSC:

32H25 (Several complex variables and analytic spaces :: Holomorphic mappings and correspondences :: Picard-type theorems and generalizations)

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