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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On one problem of uniqueness of meromorphic functions concerning small functions


Author: Hong-Xun Yi
Journal: Proc. Amer. Math. Soc. 130 (2002), 1689-1697
MSC (2000): Primary 30D35; Secondary 30D30
Published electronically: October 17, 2001
MathSciNet review: 1887016
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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, we show that if two non-constant meromorphic functions $f$ and $g$ satisfy $\overline{E}(a_{j},k,f)=\overline{E}(a_{j},k,g)$for $j=1,2,\dots ,5$, where $a_{j}$ are five distinct small functions with respect to $f$ and $g$, and $k$ is a positive integer or $\infty $ with $k\geq 14$, then $f\equiv g$. As a special case this also answers the long-standing problem on uniqueness of meromorphic functions concerning small functions.


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Additional Information

Hong-Xun Yi
Affiliation: Department of Mathematics, Shandong University, Jinan 250100, People’s Republic of China
Email: hxyi@sdu.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-01-06245-1
PII: S 0002-9939(01)06245-1
Keywords: Meromorphic function, small function, uniqueness theorem
Received by editor(s): September 22, 2000
Received by editor(s) in revised form: December 1, 2000
Published electronically: October 17, 2001
Additional Notes: This work was supported by the NSFC (NO. 19871050) and the RFDP (No. 98042209).
Communicated by: Juha M. Heinonen
Article copyright: © Copyright 2001 American Mathematical Society