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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:
 30D35 Distribution of values (one complex variable); Nevanlinna theory 30D30 General theory of meromorphic functions