## 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:

 30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory 30D30 Meromorphic functions of one complex variable (general theory)
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