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Meromorphic function that shares one small function with its differential polynomial. (English) Zbl 1206.30045
Summary: We investigate the uniqueness problem for meromorphic functions that share a small function with its differential polynomials, and give a result which is related to a conjecture of R. Brück [Result. Math. 30, No.1–2, 21–24 (1996; Zbl 0861.30032)] and improve results of I. Lahiri and A. Sarkar [JIPAM, J. Inequal. Pure Appl. Math. 5, No. 1, Paper No. 20, 9 p., electronic only (2004; Zbl 1056.30030)] and Q. C. Zhang [JIPAM, J. Inequal. Pure Appl. Math. 6, No. 4, Paper No. 116, 13 p., electronic only (2005; Zbl 1097.30033)].

MSC:
30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
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