Research articles
ScienceAsia 50 (2024):ID 2024091 1-7 |doi:
10.2306/scienceasia1513-1874.2024.091
Unicity of meromorphic functions whose lower order is finite
and noninteger
Minling Zenga,b, Ruilin Zhengc, Ge Wangb, Mingliang Fanga,b,*
ABSTRACT: In this paper, we study unicity of meromorphic functions whose lower order is finite and noninteger and
mainly prove: Let f and g be two nonconstant meromorphic functions, let n ? 6 be an integer, S = {z |
(n?1)(n?2)
4
z
n ?
n(n?2)
2
z
n?1 +
n(n?1)
4
z
n?2 ? 1 = 0}. If f and g share S, ? CM, and the lower order of f is finite and noninteger, then
f ? g. This answers a question posed by Gross for meromorphic functions whose lower order is finite and noninteger.
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a |
Department of Engineering, Shenzhen MSU-BIT University, Shenzhen 518172 China |
b |
Department of Mathematics, Hangzhou Dianzi University, Hangzhou 310018 China |
c |
Department of Mathematics and Informatics, South China Agricultural University, Guangzhou 510642 China |
* Corresponding author, E-mail: mlfang@hdu.edu.cn
Received 31 Dec 2023, Accepted 10 Aug 2024
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