Use this URL to cite or link to this record in EThOS: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.415686
Title: Complex analysis using Nevanlinna theory
Author: Alotaibi, Abdullah Mathker
ISNI:       0000 0001 3418 3499
Awarding Body: University of Nottingham
Current Institution: University of Nottingham
Date of Award: 2005
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Abstract:
In this thesis, we mainly worked in the following areas: value distributions of meromorphic functions, normal families, Bank-Laine functions and complex oscillation theory. In the first chapter we will give an introduction to those areas and some related topics that are needed. In Chapter 2 we will prove that for a meromorphic function f and a positive integer k, the function af(f(k))n -1, n ≥ 2, has infinitely many zeros and then we will prove that it is still true when we replace f(k) by a differential polynomial. In Chapter 3 we will prove that for a merornorphic function f and a positive integer k, the function af f(k) -1 with N1(r, 1/f^((k)) ) = S(r, f) has infinitely many zeros and then we will prove that it is still true when we replace f(k) by a differential polynomial. In Chapter 4 we will apply Bloch's Principle to prove that a family of functions meromorphic on the unit disc B(0, 1), such that f(f1)m≠ 1, m ≠ 2, is normal. Also we will prove that a family of functions meromorphic on B(0,1), such that each f ≠ 0 and f(f(k))m ,k, m ∈N omits the value 1, is normal. In the fifth chapter we will generalise Theorem 5.1.1 for a sequence of distinct complex numbers instead of a sequence of real numbers. Also, we will get very nice new results on Bank-Laine functions and Bank-Laine sequences. In the last chapter we will work on the relationship between the order of growth of A and the exponent of convergence of the solutions y(k) +Ay =0, where A is a transcendental entire function with ρ(A) < 1/2.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.415686  DOI: Not available
Keywords: QA299 Analysis
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