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    Please use this identifier to cite or link to this item: http://nccur.lib.nccu.edu.tw/handle/140.119/54039

    Title: 半純函數之值分佈與其相關問題
    Other Titles: Value Distribution of Meromorphic Functions and Its Related Problems
    Authors: 陳天進
    Contributors: 國立政治大學應用數學學系
    Keywords: 數學
    Date: 2008
    Issue Date: 2012-10-24 16:13:40 (UTC+8)
    Abstract: Hayman 猜測對於任意的超越半純函數f (z), f ' (z) f (z)n 取任意非零的值無窮多次,因此,很自然的問題是f (k ) (z) f (z)n,其中k 2,具有相同的結果;同時,在文獻上我們也知道f(z)af (z)n 取任意非零的值無窮多次,所以,我們也將探討 f (k ) (z)af (z)n的值分佈,這些是本計畫研究的一部分。另外,本計畫也將著重於兩個半純函數共值或共小函數的問題進行研究。
    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. Therefore, it is natural to ask what is the value distribution of f (k ) (z) f (z)n ? Also, we know that f(z)af (z)n assumes all finite values except possibly zero infinitely often. So, we can ask the same question for f (k ) (z)af (z)n . This is a part of the project which we will study. Another part is to study the problems of sharing values (small functions) of two meromorphic functions.
    Relation: 基礎研究
    研究期間:9708~ 9807
    Data Type: report
    Appears in Collections:[應用數學系] 國科會研究計畫

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