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Langley, James (2016)
Publisher: Springer
Languages: English
Types: Article
Subjects: 30D35, Mathematics - Complex Variables

Classified by OpenAIRE into

arxiv: Mathematics::Complex Variables, Mathematics::Metric Geometry
Consider a transcendental meromorphic function in the plane with finitely many critical values, such that the multiple points have bounded multiplicities and the inverse function has finitely many transcendental singularities. Using the Wiman-Valiron method it is shown that if the Schwarzian derivative is transcendental then the function has infinitely many multiple points, the inverse function does not have a direct transcendental singularity over infinity, and infinity is not a Borel exceptional value. The first of these conclusions was proved by Nevanlinna and Elfving via a fundamentally different method.
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