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The Schwarzian derivative and the Wiman-Valiron property

Langley, James


James Langley


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.


Langley, J. (in press). The Schwarzian derivative and the Wiman-Valiron property. Journal d'Analyse Mathématique, 130(1),

Journal Article Type Article
Acceptance Date Aug 15, 2013
Online Publication Date Nov 22, 2016
Deposit Date Nov 24, 2016
Publicly Available Date Nov 24, 2016
Journal Journal d'Analyse Mathématique
Print ISSN 0021-7670
Electronic ISSN 1565-8538
Publisher Springer Verlag
Peer Reviewed Peer Reviewed
Volume 130
Issue 1
Public URL
Publisher URL
Additional Information The final publication is available at Springer via


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