Acta Mathematica Sinica

, Volume 12, Issue 2, pp 191–204

# On the order of a class of meromorphic functions

• Wu Pengcheng
Article

## Abstract

This paper proves the following result: Letf(z) be a meromorphic function in thez-plane with a deficient value, and δ(θ k )(k=1,2, ...,q;0≤θ12<...<θq<θq+1=θ1+2π) beq rays (1≤q<∞) starting at the origin, and letn≥3 be an integer such that for any given positive numberε,0<ε<π/2,
$$\overline {\mathop {\lim }\limits_{r \to \infty } } \frac{{\log ^ + n\left\{ { \cup _{k = 1}^q \Omega \left( {\theta _k + \varepsilon ,\theta _{k + 1} - \varepsilon ,r} \right),f\prime f^n = 1} \right\}}}{{\log r}} \leqslant v< \infty ,$$
whereΝ is a constant independent ofε. IfΜ<∞, then we have
$$\lambda \leqslant \frac{\pi }{\omega } + v,$$
whereΜ andλ denote the lower order and order off(z), respectively,Ω=minθ k+1 −θ k ;1≤k≤q, andn(E, f=a) is the number of zeros off(z)−a inE with multiple zeros being counted with their multiplicities.

## Keywords

Meromorphic function Order

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