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| Title: | 半純函數與其導數之值分佈
On The Value Distribution Of Meromorphic Functions With Their Derivatives |
| Authors: | 歐姿君
Ou, Tze Chun |
| Contributors: | 陳天進
Chen, Ten Ging
歐姿君
Ou, Tze Chun |
| Keywords: | 值分佈理論
半純函數
value distribution theory
meromorphic function |
| Date: | 2007 |
| Issue Date: | 2009-09-17 13:48:01 (UTC+8) |
| Abstract: | Haymen猜測:對任意的超越半純函數 f(z)，f`(z)f(z)^n 取所有值無窮多次，其中至多只有一個例外值。這個著名的猜測，大部分的情形已被證明是正確的。另外，Hayman 證明 f`(z)-af(z)^n 取所有有限值無窮多次
，其中 a 為一複數且 n≧5 的正整數。在本篇論文裡，我們將探討以小函數為係數的半純函數微分多項式之值分佈問題。並將Hayman的結果推廣至 f^{k}(z)f(z)^n 與 f^{k}(z)-af(z)^n 的情形。同時，我們也證明一些
A類半純函數與其導數的值分佈結果。
A famous conjecture of Hayman says that if f(z) is a transcendental meromorphic function, then f`(z)f(z)^n assumes all finite values except possibly zero infinitely often. The conjecture was solved in most cases. Another result of Hayman says that f`(z)-af(z)^n, where n≧5 and a is a complex number, assumes all finite values infinitely often. In this thesis, we will study the value distribution of some differential polynomial in a meromorphic function with small functions as coefficents. In fact, we will generalize Hayman`s results to the cases f^(k)(z)f(z)^n and f^(k)(z)-af(z)^n. Also, the value distribution of meromorphic functions of class A with their derivatives are obtained. |
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thesis, National Chengchi University, 2007. |
| Description: | 碩士
國立政治大學
應用數學研究所
94751008
96 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#G0094751008 |
| Data Type: | thesis |
| Appears in Collections: | [應用數學系] 學位論文
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