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Critical Values of Slowly Growing Meromorphic Functions

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Abstract

Let f be transcendental and meromorphic in the plane. We obtain sharp lower bounds for the growth of f, in terms of the minimum spherical distance between the critical values of f. The extremal examples arise from elliptic functions.

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Correspondence to James K. Langley.

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Langley, J.K. Critical Values of Slowly Growing Meromorphic Functions. Comput. Methods Funct. Theory 2, 539–547 (2004). https://doi.org/10.1007/BF03321864

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