The Schwarzian derivative and the Wiman-Valiron property

2013/07/11 by J. K. Langley, Langley, J. K.
Mathematics · #30D35 #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Mathematics and Applications #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.1307.3042

openalex publication_date 2013/07/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Suppose that a transcendental meromorphic function in the plane has finitely many critical values, while its multiple points have bounded multiplicities, and its inverse function has finitely many transcendental singularities. Using the Wiman-Valiron method it is shown that the Schwarzian derivative does not have a direct transcendental singularity over infinity, and does not have infinity as a Borel exceptional value.

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