Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2016; 53(2): 365-371

Printed March 31, 2016

https://doi.org/10.4134/BKMS.2016.53.2.365

Copyright © The Korean Mathematical Society.

A note on the value distribution of $f^2(f')^n$ for $n\geq 2$

Yan Jiang

Tohoku University

Abstract

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 $N(r,1/(f^2(f')^n-a))$, which states as following inequality, for positive integers $n\geq 2$, $$T(r,f)\leq \left(3+\frac{6}{n-1}\right)N\left(r,\frac{1}{af^2(f')^n-1}\right)+S(r,f).$$

Keywords: transcendental meromorphic function, deficiency

MSC numbers: Primary 30D35

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