In this paper,we improve a more recent functions and its shifts due to Heittokangas etc. J. J. Rieppo and J. Zhang, Value sharing results for sufficient conditions for periodicity, J. Math. Anal. uniqueness theorem on meromorphic Heittokanga~s, R. Korhonen, I. Laine. shifts of meromorphic function and Appl., 355 (2009): 352-363].%改进Heittokangas等最近获得的涉及亚纯函数与其平移函数唯一性的一个结果[J.Heit-tokangas,R.Korhonen,I.Laine,J.Rieppo and J.Zhang,Value sharing results for shifts of mero-morphic function and sufficient conditions for periodicity,J.Math.Anal.Appl.,355(2009):352-363].
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