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On the uniqueness of meromorphic functions that share four values in one angular domain. (English) Zbl 1167.30012

Summary: The main purpose of this paper is to investigate the uniqueness of transcendental meromorphic functions that share four values in an angular domain which is an unbounded subset of the whole complex plane. From one of our main results, a question of J.-H. Zheng [Complex Variables, Theory Appl. 48, No. 9, 777–785 (2003; Zbl 1041.30009)] is completely answered. Furthermore, we give an example to explain the necessity of the condition

lim r S α,β (r,f) log(rT(r,f))=

in our result.


MSC:
30D35Distribution of values (one complex variable); Nevanlinna theory