Uniqueness of p(f) and P[f]

2015/01/21 by Charak, Kuldeep Singh, Lal, Banarsi
#30D30 #30D35 #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1501.05092

Abstract

Let f be a non constant meromorphic function and a(not identically zero or infinity) be a meromorphic function satisfying T(r,a) = o(T(r,f)) as r tends to infinity, and p(z) be a polynomial of degree n greater than or equal to 1 with p(0) = 0. Let P[f] be a non constant differential polynomial of f. Under certain essential conditions, we prove the uniqueness of p(f) and P[f] when p(f) and P[f] share a with weight l greater than or equal to zero. Our result generalizes the results due to Zang and Lu, Banerjee and Majumder, Bhoosnurmath and Kabbur and answers a question of Zang and Lu.

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