Abstract
<abstract><p>In this paper, we prove that two admissible meromorphic functions on an annulus must be linked by a quasi-Möbius transformation if they share some pairs of small function with multiplicities truncated by $ 4 $. We also give the representation of Möbius transformation between two admissible meromorphic functions on an annulus if they share four pairs of values with multiplicities truncated by $ 4 $. In our results, the zeros with multiplicities more than a certain number are not needed to be counted if their multiplicities are bigger than a certain number.</p></abstract>
Publisher
American Institute of Mathematical Sciences (AIMS)
Reference15 articles.
1. T. B. Cao, Z. S. Deng, On the uniqueness of meromorphic functions that share three or two finite sets on annuli, Proc. Indian Acad. Sci., 122 (2012), 203–220.
2. T. B. Cao, H. X. Yi, H. Y. Xu, On the multiple values and uniqueness of meromorphic functions on annuli, Comput. Math. Appl., 58 (2009), 1457–1465.
3. T. Czubiak, G. Gundersen, Meromorphic functions that share pairs of values, Complex Var. Elliptic Equ., 34 (1997), 35–46.
4. A. Y. Khrystiyanyn, A. A. Kondratyuk, On the Nevanlinna theory for meromorphic functions on annuli I, Mat. Stud., 23 (2005), 19–30.
5. A. Y. Khrystiyanyn, A. A. Kondratyuk, On the Nevanlinna theory for meromorphicfunctions on annuli II, Mat. Stud., 24 (2005), 57–68.