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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