一类特殊亚纯函数的唯一性象集
Unique Range Sets for a Kind of Special Meromorphic Functions
DOI: 10.12677/PM.2020.102011, PDF,   
作者: 李荣慧*, 胡 岚：云南师范大学数学学院，云南 昆明
关键词: 亚纯函数；分担值集；唯一性；Meromorphic Functions； Shared Set； Uniqueness
摘要: 本文讨论了关于一类特殊亚纯函数元素个数较少的唯一性象集问题。证明了：设集合S={z:z6+z5+1=0},f(z)和g(z)为非常数亚纯函数，且满足Ef(S)=Eg(S)。当对f(z)和g(z)附加特定的条件后，则有f(z)=g(z)。
Abstract: In this paper, we discuss the problem of unique range sets with fewer elements for a kind of special meromorphic functions. The following result is proved: Let S={z:z6+z5+1=0} be a set such that two nonconstant meromorphic functions f(z) and g(z) satisfy Ef(S)=Eg(S). If we attach certain conditions to f(z) and g(z), then f(z)=g(z).
文章引用：李荣慧, 胡岚. 一类特殊亚纯函数的唯一性象集[J]. 理论数学, 2020, 10(2): 65-71. https://doi.org/10.12677/PM.2020.102011

参考文献

[1] 杨乐. 值分布论及其新研究[M]. 北京: 科学出版社, 1982.
[2] 仪洪勋, 杨重骏. 亚纯函数唯一性理论[M]. 北京: 科学出版社, 1995.
[3] Gross, F. and Yang, C.C. (1982) On Preimage and Range Sets of Meromorphic Functions. Proceedings of the Japan Academy, Ser. A, Mathematical Sciences, 58, 17-20. [Google Scholar] [CrossRef] 
[4] Gross, F. (1977) Factorization of Meromorphic Function and Some Open Problems. In: Complex Analysis, Lecture Notes in Math, Vol. 599, Springer, Berlin, Heidelberg, New York, 51-69. [Google Scholar] [CrossRef] 
[5] Yi, H.X. (1995) On a Question of Gross. Science in China (Ser A), 38, 8-16.
[6] Yi, H.X. (1995) A Question of Gross and the Uniqueness of Entire Functions. Nagoya Mathematical Journal, 138, 169-177. [Google Scholar] [CrossRef] 
[7] 仪洪勋. 关于亚纯函数的精简唯一性象集[J]. 山东大学学报(自然科学版), 1998, 33(4): 361-369.
[8] Fang, M.L. and Hua, X.H. (1998) Meromorpic Functions That Share One Finite Set CM. Journal of Nanjing University Mathematical Biquarterly, 15, 16-22.
[9] 杨力. 一类整函数的唯一性象集[J]. 纺织高校基础科学学报, 2000, 13(3): 198-201.
[10] 王新利. 具有一个CM公共值集的亚纯函数[J]. 山东大学学报, 2001, 36(1): 5-10.
[11] Xu, Y. (2003) Meromorphic Functions Sharing One Finite Set. Computers and Mathematics with Applications, 45, 1489-1495. [Google Scholar] [CrossRef] 
[12] 段曦盛. 亚纯函数的几个唯一性定[D]: [硕士学位论文]. 重庆: 重庆大学, 2004.
[13] 白小甜. 关于亚纯函数分担公共值集的一些结果[D]: [博士学位论文]. 济南: 山东大学, 2011.
[14] 熊坚. 关于亚纯函数的分担值集与唯一性[D]: [硕士学位论文]. 昆明: 云南师范大学, 2008.
[15] Yi, H.X. (1994) Unicity Theorems for Entire Functions. Kodai Mathematical Journal, 17, 133-141. [Google Scholar] [CrossRef] 

为你推荐