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- W2032009974 abstract "Let $$kin mathbb{N }$$ and $$h(not equiv 0)$$ be a function holomorphic on $$D$$ . Let $$mathcal{F }$$ be a family of meromorphic functions in $$D$$ , all of whose zeros have multiplicity at least $$k+3$$ . Suppose that the sets $${E_f}_{fin mathcal{F }}$$ are locally uniformly discrete in $$D$$ , where $$E_f={zin D:f(z)=0}cup {zin D:f^{(k)}(z)=h(z)}$$ . Suppose additionally that at the common zeros of $$fin mathcal{F }$$ and $$h$$ , the multiplicities $$m_f$$ for $$f$$ and $$m_h$$ for $$h$$ satisfy $$m_fge m_h+k+1$$ for $$k>1$$ and $$m_fge 2m_h+3$$ for $$k=1$$ . Then, $$mathcal{F }$$ is normal in $$D$$ . The number $$k+3$$ can be replaced by $$k+2$$ if the set $$E_f$$ is independent of $$f$$ , or in other words, for each pair of functions $$f$$ and $$g$$ in $$mathcal{F }$$ , $$f$$ and $$g$$ share the value $$0$$ , and $$f^{(k)}$$ and $$g^{(k)}$$ share the function $$h$$ . Examples are also given to show that the conditions are necessary and sharp." @default.
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- W2032009974 date "2013-01-23" @default.
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- W2032009974 title "Normality of Meromorphic Functions and Uniformly Discrete Exceptional Sets" @default.
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- W2032009974 doi "https://doi.org/10.1007/s40315-012-0003-x" @default.
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