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On uniqueness of meromorphic functions with shared values in some angular domains. (English) Zbl 1045.30019
Two meromorphic functions f and g are said to share a value a if they have the same a-points. A classical result of Nevanlinna says that if f and g share five values, then f=g· Here it is shown that if f has finite lower order and if f or some derivative of f has a deficient value, then it suffices to assume that f and g share five values outside certain sectors in order to conclude that f=g· The size and configuration of these sectors depend on the lower order of f and on the deficiency. Such a result does not hold if f has infinite (lower) order, but for this case a similar result is given where f and g share five values outside certain rays. The proofs use, among other things, Nevanlinna theory in angular domains.

MSC:
30D35Distribution of values (one complex variable); Nevanlinna theory
30D30General theory of meromorphic functions