Some results on the value distribution of meromorphic functions

Hinchliffe, James David (2003) Some results on the value distribution of meromorphic functions. PhD thesis, University of Nottingham.

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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.

Item Type: Thesis (University of Nottingham only) (PhD)
Supervisors: Langley, J.K.
Keywords: complex analysis, nevanlinna theory, nevanlinna, value distribution, meromorphic functions, meromorphic
Subjects: Q Science > QA Mathematics > QA299 Analysis
Faculties/Schools: UK Campuses > Faculty of Science > School of Mathematical Sciences
Item ID: 10043
Depositing User: EP, Services
Date Deposited: 06 Jan 2004
Last Modified: 15 Oct 2017 14:41

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