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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.
Computational Methods and Function Theory – Springer Journals
Published: Jan 25, 2012
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