The Schwarzian derivative and the Wiman-Valiron property
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 derivat...
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| Format: | Article |
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Springer
2016
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| Online Access: | https://eprints.nottingham.ac.uk/38915/ |
| _version_ | 1848795719899545600 |
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| author | Langley, James |
| author_facet | Langley, James |
| author_sort | Langley, James |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T19:36:34Z |
| format | Article |
| id | nottingham-38915 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:36:34Z |
| publishDate | 2016 |
| publisher | Springer |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-389152020-05-04T18:20:20Z https://eprints.nottingham.ac.uk/38915/ The Schwarzian derivative and the Wiman-Valiron property Langley, James 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. Springer 2016-11-22 Article PeerReviewed Langley, James (2016) The Schwarzian derivative and the Wiman-Valiron property. Journal d'Analyse Mathématique, 130 (1). pp. 71-89. ISSN 1565-8538 http://link.springer.com/article/10.1007/s11854-016-0029-5 doi:10.1007/s11854-016-0029-5 doi:10.1007/s11854-016-0029-5 |
| spellingShingle | Langley, James The Schwarzian derivative and the Wiman-Valiron property |
| title | The Schwarzian derivative and the Wiman-Valiron property |
| title_full | The Schwarzian derivative and the Wiman-Valiron property |
| title_fullStr | The Schwarzian derivative and the Wiman-Valiron property |
| title_full_unstemmed | The Schwarzian derivative and the Wiman-Valiron property |
| title_short | The Schwarzian derivative and the Wiman-Valiron property |
| title_sort | schwarzian derivative and the wiman-valiron property |
| url | https://eprints.nottingham.ac.uk/38915/ https://eprints.nottingham.ac.uk/38915/ https://eprints.nottingham.ac.uk/38915/ |