대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제53권2호
  • /
  • Pages.365-371
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  • 2016
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  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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A NOTE ON THE VALUE DISTRIBUTION OF f2(f')n FOR n≥2

  • Jiang, Yan (Graduate School of Information Sciences, Tohoku University)
  • 투고 : 2014.05.21
  • 발행 : 2016.03.31
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초록

Let f be a transcendental meromorphic function in the complex plane $\mathbb{C}$, and a be a nonzero constant. We give a quantitative estimate of the characteristic function T(r, f) in terms of $N(r,1/(f^2(f^{\prime})^n-a))$, which states as following inequality, for positive integers $n{\geq}2$, $$T(r,f){\leq}\(3+{\frac{6}{n-1}}\)N\(r,{\frac{1}{af^2(f^{\prime})^n-1}}\)+S(r,f)$$.

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참고문헌

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피인용 문헌

  1. On the Zeros of the Differential Polynomial φ(z)f2(z)f′(z)2 − 1 vol.7, pp.1, 2019, https://doi.org/10.3390/math7010087