Some results on the value distribution of meromorphic functions
In Chapter 1 we introduce many of the concepts and techniques, including Nevanlinna theory, referred to throughout the rest of the thesis. In Chapter 2 we extend a result of Langley and Shea concerning the distribution of zeros of the logarithmic derivative of meromorphic functions to higher order...
| Main Author: | |
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| Format: | Thesis (University of Nottingham only) |
| Language: | English |
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2003
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| Online Access: | https://eprints.nottingham.ac.uk/10043/ |
| _version_ | 1848791013608390656 |
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| author | Hinchliffe, James David |
| author_facet | Hinchliffe, James David |
| author_sort | Hinchliffe, James David |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | In Chapter 1 we introduce many of the concepts and techniques, including Nevanlinna theory, referred to throughout the rest of the thesis. In Chapter 2 we extend a result of Langley and Shea concerning the distribution of zeros of the logarithmic derivative of meromorphic functions to higher order logarithmic derivatives. Chapter 3 details an alternative formulation, avoiding reference to the multiplicity of poles, of a result due to Chuang concerning differential polynomials. In Chapter 4 we generalise a theorem of Bergweiler and Eremenko concerning transcendental singularities of the the inverse of a meromorphic function. In Chapter 5 we generalise a result of Gordon to show that an unbounded analytic function on a quasidisk has a strong form of unboundedness there. Chapter 6 contains a proof of a result concerning the normality of families of analytic functions such that the composition of any of these functions with a fixed (meromorphic) outer factor has no fixpoints in a given domain. |
| first_indexed | 2025-11-14T18:21:46Z |
| format | Thesis (University of Nottingham only) |
| id | nottingham-10043 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T18:21:46Z |
| publishDate | 2003 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-100432025-02-28T11:06:58Z https://eprints.nottingham.ac.uk/10043/ Some results on the value distribution of meromorphic functions Hinchliffe, James David In Chapter 1 we introduce many of the concepts and techniques, including Nevanlinna theory, referred to throughout the rest of the thesis. In Chapter 2 we extend a result of Langley and Shea concerning the distribution of zeros of the logarithmic derivative of meromorphic functions to higher order logarithmic derivatives. Chapter 3 details an alternative formulation, avoiding reference to the multiplicity of poles, of a result due to Chuang concerning differential polynomials. In Chapter 4 we generalise a theorem of Bergweiler and Eremenko concerning transcendental singularities of the the inverse of a meromorphic function. In Chapter 5 we generalise a result of Gordon to show that an unbounded analytic function on a quasidisk has a strong form of unboundedness there. Chapter 6 contains a proof of a result concerning the normality of families of analytic functions such that the composition of any of these functions with a fixed (meromorphic) outer factor has no fixpoints in a given domain. 2003 Thesis (University of Nottingham only) NonPeerReviewed application/pdf en arr https://eprints.nottingham.ac.uk/10043/1/thesis.pdf Hinchliffe, James David (2003) Some results on the value distribution of meromorphic functions. PhD thesis, University of Nottingham. complex analysis nevanlinna theory nevanlinna value distribution meromorphic functions meromorphic |
| spellingShingle | complex analysis nevanlinna theory nevanlinna value distribution meromorphic functions meromorphic Hinchliffe, James David Some results on the value distribution of meromorphic functions |
| title | Some results on the value distribution of meromorphic functions |
| title_full | Some results on the value distribution of meromorphic functions |
| title_fullStr | Some results on the value distribution of meromorphic functions |
| title_full_unstemmed | Some results on the value distribution of meromorphic functions |
| title_short | Some results on the value distribution of meromorphic functions |
| title_sort | some results on the value distribution of meromorphic functions |
| topic | complex analysis nevanlinna theory nevanlinna value distribution meromorphic functions meromorphic |
| url | https://eprints.nottingham.ac.uk/10043/ |