Rubel-Yang-Mues-Steinmetz-Gundersen定理的一个不同版本

IF 0.6 4区 数学 Q3 MATHEMATICS
Mingliang Fang, Hui Li, Wenqiang Shen, Xiao Yao
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引用次数: 0

摘要

本文给出了具有三个不同值\(a,\,b,\,\infty \) CM的亚纯函数及其差分算子\(\Delta _c f\)或位移\(f(z+c)\)的完整刻划。这提供了Rubel-Yang, Mues-Steinmetz和Gundersen相应结果的不同模拟。特别地,我们证明了如果整个函数f和它的差分导数\(\Delta _c f\)共享三个不同的值\(a,\,b,\,\infty \) CM,那么\(f\equiv \Delta _c f\)。我们的结果表明Chen和Yi在2013年提出的猜想对整个函数成立,而对亚纯函数不成立。与以往的许多论文相比,我们的方法绕过了无限阶亚纯函数的差分对数导数引理的障碍,因为该方法不依赖于函数的增长,而需要线性代数和组合学的知识。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

A Difference Version of the Rubel-Yang–Mues-Steinmetz–Gundersen Theorem

A Difference Version of the Rubel-Yang–Mues-Steinmetz–Gundersen Theorem

In this paper, we give a complete characterization for meromorphic functions that share three distinct values \(a,\,b,\,\infty \) CM, with their difference operator \(\Delta _c f\) or shift \(f(z+c)\). This provides a difference analogue of the corresponding results of Rubel-Yang, Mues-Steinmetz, and Gundersen. In particular, we prove that if an entire function f and its difference derivative \(\Delta _c f\) share three distinct values \(a,\,b,\,\infty \) CM, then \(f\equiv \Delta _c f\). And our results show that the conjecture posed by Chen and Yi in 2013 holds for entire functions, and does not hold for meromorphic functions. Compared with many previous papers, our method circumvents the obstacle of the difference logarithmic derivative lemma for meromorphic functions of infinite order, since this method does not depend on the growth of the functions, but requires the knowledge of linear algebra and combinatorics.

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来源期刊
Computational Methods and Function Theory
Computational Methods and Function Theory MATHEMATICS, APPLIED-MATHEMATICS
CiteScore
3.20
自引率
0.00%
发文量
44
审稿时长
>12 weeks
期刊介绍: CMFT is an international mathematics journal which publishes carefully selected original research papers in complex analysis (in a broad sense), and on applications or computational methods related to complex analysis. Survey articles of high standard and current interest can be considered for publication as well.
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