Two meromorphic functions sharing four pairs of small functions
Bull. Korean Math. Soc. 2017 Vol. 54, No. 4, 1159-1171
Published online July 31, 2017
Van An Nguyen and Duc Quang Si
Banking Academy, Hanoi National University of Education
Abstract : The purpose of this paper is twofold. The first is to show that two meromorphic functions $f$ and $g$ must be linked by a quasi-M\"{o}bius transformation if they share a pair of small functions regardless of multiplicity and share other three pairs of small functions with multiplicities truncated to level 4. We also show a quasi-M\"{o}bius transformation between two meromorphic functions if they share four pairs of small functions with multiplicities truncated by $4$, where all zeros with multiplicities at least $k> 865$ are omitted. Moreover the explicit M\"{o}bius-transformation between such $f$ and $g$ is given. Our results are improvement of some recent results.
Keywords : meromorphic function, small function, M\"{o}bius transformation
MSC numbers : Primary 32H30, 32A22; Secondary 30D35
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