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 A note on the value distribution of Differential Polynomials Commun. Korean Math. Soc.Published online June 7, 2019 SUBHAS S. BHOOSNURMATH, BIKASH CHAKRABORTY, and H. M. SRIVASTAVA Karnatak University, Ramakrishna Mission Vivekananda Centenary College, University of Victoria Abstract : Let $f$ be a transcendental meromorphic function, defined in $\mathbb{C}$. In this paper, we give quantitative estimations of the characteristic function $T(r,f)$ in terms of the counting function of a homogeneous differential polynomial generated by $f$. Our result improves and generalizes some recent results. Keywords : Transcendental Meromorphic function, Differential Polynomials MSC numbers : 30D35 Full-Text :