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Normal families and shared values of meromorphic functions

Mingliang FangLawrence Zalcman — 2003

Annales Polonici Mathematici

Let ℱ be a family of meromorphic functions on a plane domain D, all of whose zeros are of multiplicity at least k ≥ 2. Let a, b, c, and d be complex numbers such that d ≠ b,0 and c ≠ a. If, for each f ∈ ℱ, f ( z ) = a f ( k ) ( z ) = b , and f ( k ) ( z ) = d f ( z ) = c , then ℱ is a normal family on D. The same result holds for k=1 so long as b≠(m+1)d, m=1,2,....

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