Journal d'Analyse Mathématique

, Volume 130, Issue 1, pp 71–89 | Cite as

The Schwarzian derivative and the Wiman-Valiron property



Let f be a transcendental meromorphic function in the plane such that f has finitely many critical values, the multiple points of f have bounded multiplicities, and the inverse function of f has finitely many transcendental singularities. Using the Wiman-Valiron method, it is shown that if the Schwarzian derivative Sf of f is transcendental, then f has infinitely many multiple points, the inverse function of Sf does not have a direct transcendental singularity over ∞, and ∞ is not a Borel exceptional value of Sf. The first of these conclusions was proved by Nevanlinna and Elfving via a fundamentally different method.


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© Hebrew University Magnes Press 2016

Authors and Affiliations

  1. 1.School of Mathematical SciencesUniversity of NottinghamNottinghamEngland

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