The Schwarzian derivative and the Wiman-Valiron property

Langley, James

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.

Citation

Langley, J. (in press). The Schwarzian derivative and the Wiman-Valiron property. Journal d'Analyse Mathématique, 130(1), https://doi.org/10.1007/s11854-016-0029-5

• 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
• DOI: https://doi.org/10.1007/s11854-016-0029-5
• Public URL: https://nottingham-repository.worktribe.com/output/827426
• Publisher URL: http://link.springer.com/article/10.1007/s11854-016-0029-5
• Additional Information: The final publication is available at Springer via http://dx.doi.org/10.1007/s11854-016-0029-5
• Contract Date: Nov 24, 2016