Uniqueness theorems for meromorphic functions on annuli

Abstract

In this paper, we discuss the uniqueness problems of meromorphic functions on annuli. We prove a general theorem on the uniqueness of meromorphic functions on annuli. An analogue of a famous Nevanlinna's five-value theorem is proposed. The main result in this paper is an analog of a result on the plane $\mathbb{C}$ obtained by H.S. Gopalkrishna and Subhas S. Bhoosnurmath for an annuli. That is, let $f_{1}(z)$ and $f_{2}(z)$ be two transcendental meromorphic functions on the annulus $\mathbb{A}=\left\{z:\frac{1}{R_{0}}<|z|2, \end{equation*} then $f_{1}(z)\equiv f_{2}(z).$