Abstract
Let S denote the class of functions f which are transcendental and meromorphic in the plane and have finitely many critical and asymptotic values. It is shown that if f ∈ S has finite lower order and f″/f′ is non-constant then δ(0, f″/f′) = 0. Moreover, the Gol’dberg conjecture holds for a function in S of finite order, at least on a set of logarithmic density 1.
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Langley, J. Meromorphic Functions in the Class S and the Zeros of the Second Derivative. Comput. Methods Funct. Theory 8, 73–84 (2008). https://doi.org/10.1007/BF03321671
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DOI: https://doi.org/10.1007/BF03321671