In this paper, we prove that two admissible meromorphic functions on an annulus must be linked by a quasi-Möbius transformation if they share some pairs of small function with multiplicities truncated by $ 4 $. We also give the representation of Möbius transformation between two admissible meromorphic functions on an annulus if they share four pairs of values with multiplicities truncated by $ 4 $. In our results, the zeros with multiplicities more than a certain number are not needed to be counted if their multiplicities are bigger than a certain number.
Citation: Hongzhe Cao. Two meromorphic functions on annuli sharing some pairs of small functions or values[J]. AIMS Mathematics, 2021, 6(12): 13311-13326. doi: 10.3934/math.2021770
In this paper, we prove that two admissible meromorphic functions on an annulus must be linked by a quasi-Möbius transformation if they share some pairs of small function with multiplicities truncated by $ 4 $. We also give the representation of Möbius transformation between two admissible meromorphic functions on an annulus if they share four pairs of values with multiplicities truncated by $ 4 $. In our results, the zeros with multiplicities more than a certain number are not needed to be counted if their multiplicities are bigger than a certain number.
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Hongzhe Cao. Two meromorphic functions on annuli sharing some pairs of small functions or values[J]. AIMS Mathematics, 2021, 6(12): 13311-13326. doi: 10.3934/math.2021770
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