The Schwarzian derivative and the Wiman-Valiron property

Langley, James (2016) The Schwarzian derivative and the Wiman-Valiron property. Journal d'Analyse Mathématique, 130 (1). pp. 71-89. ISSN 1565-8538

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Abstract

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.

Item Type: Article
Additional Information: The final publication is available at Springer via http://dx.doi.org/10.1007/s11854-016-0029-5
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences
Identification Number: https://doi.org/10.1007/s11854-016-0029-5
Depositing User: Langley, James
Date Deposited: 24 Nov 2016 09:31
Last Modified: 24 Nov 2016 09:38
URI: http://eprints.nottingham.ac.uk/id/eprint/38915

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