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A note on the value distribution of differential polynomials
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Let $f$ be a transcendental meromorphic function, defined in the complex plane $\mathbb{C}$. In this paper, we give a 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.
Abstract
Let $f$ be a transcendental meromorphic function, defined in the complex plane $\mathbb{C}$. In this paper, we give a 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.
참고문헌 (9)
- "2018", ~
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- Nan Li, "Meromorphic Function that Shares One Small Function with its Differential Polynomial", Kyungpook Mathematical Journal, 50(3), pp.447~454 (2010), 경북대학교 자연과학대학 수학과
- Erwin Mues, "Uber ein Problem von Hayman", Mathematische Zeitschrift, 164(3), pp.239~259 (1979), Springer Science and Business Media LLC[DOI]
- K. Yamanoi, "Zeros of higher derivatives of meromorphic functions in the complex plane", Proc. Lond. Math. Soc. (3), 106(4), pp.703~780 (2013)[DOI]
- Q. D. Zhang, "A growth theorem for meromorphic functions", J. Chengdu Inst. Meteor, 20, pp.12~20 (1992)
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