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.

[img]
Preview
PDF
691Kb

Abstract

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 (PhD)
Supervisors:Langley, J.K.
Uncontrolled Keywords:complex analysis, nevanlinna theory, nevanlinna, value distribution, meromorphic functions, meromorphic
Faculties/Schools:UK Campuses > Faculty of Science > School of Mathematical Sciences
ID Code:43
Deposited By:James Hinchliffe
Deposited On:06 Jan 2004
Last Modified:06 Feb 2009 14:43

Repository Staff Only: item control page