Complex analysis using Nevanlinna theory
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...
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| Format: | Thesis (University of Nottingham only) |
| Language: | English |
| Published: |
2005
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| Online Access: | https://eprints.nottingham.ac.uk/13793/ |
| _version_ | 1848791808553779200 |
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| author | Alotaibi, Abdullah Mathker |
| author_facet | Alotaibi, Abdullah Mathker |
| author_sort | Alotaibi, Abdullah Mathker |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T18:34:24Z |
| format | Thesis (University of Nottingham only) |
| id | nottingham-13793 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T18:34:24Z |
| publishDate | 2005 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-137932025-02-28T11:27:03Z https://eprints.nottingham.ac.uk/13793/ Complex analysis using Nevanlinna theory Alotaibi, Abdullah Mathker 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. 2005-07-11 Thesis (University of Nottingham only) NonPeerReviewed application/pdf en arr https://eprints.nottingham.ac.uk/13793/1/415686.pdf Alotaibi, Abdullah Mathker (2005) Complex analysis using Nevanlinna theory. PhD thesis, University of Nottingham. |
| spellingShingle | Alotaibi, Abdullah Mathker Complex analysis using Nevanlinna theory |
| title | Complex analysis using Nevanlinna theory |
| title_full | Complex analysis using Nevanlinna theory |
| title_fullStr | Complex analysis using Nevanlinna theory |
| title_full_unstemmed | Complex analysis using Nevanlinna theory |
| title_short | Complex analysis using Nevanlinna theory |
| title_sort | complex analysis using nevanlinna theory |
| url | https://eprints.nottingham.ac.uk/13793/ |