Please use this identifier to cite or link to this item: `https://ah.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行政院國家科學委員會 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: 基礎研究學術補助研究期間:9708~ 9807研究經費:317仟元 Data Type: report Appears in Collections: [應用數學系] 國科會研究計畫

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