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A proof of the great Picard theorem. (English) Zbl 1069.30047
Great Picard Theorem: If \(z_0\) is a point of the Riemann sphere \(\mathbb C^*\) and \(f\) is a function which is holomorphic in a punctured neighborhood of \(z_0\) and has an essential singularity at \(z_0\) then in every neighborhood of \(z_0\) the function \(f\) takes every complex value, with at most one exception, infinitely many times.
The author gives a simple and self contained proof of the Great Picard Theorem based on certain Harnack-type inequalities due to J. Lewis.
MSC:
30D20 Entire functions of one complex variable (general theory)
30D45 Normal functions of one complex variable, normal families
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Full Text: Euclid