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Zeros of Derivatives of Real Meromorphic Functions

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Abstract

Two results are proved for real meromorphic functions in the plane. First, a lower bound is given for the distance between distinct non-real poles when the function and its second derivative have finitely many non-real zeros and the logarithmic derivative has finite lower order. Second, if the function has finitely many non-real zeros, and one of its higher derivatives has finitely many zeros in the plane, and if the multiplicities of non-real poles grow sufficiently slowly, then the function is a rational function multiplied by the exponential of a polynomial.

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  1. School of Mathematical Sciences, University of Nottingham, NG7 2RD, UK

    Jim Langley

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Langley, J. Zeros of Derivatives of Real Meromorphic Functions. Comput. Methods Funct. Theory 12, 241–256 (2012). https://doi.org/10.1007/BF03321825

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