Abstract
Letf be a real meromorphic function of infinite order in the plane such thatf has finitely many poles. Then for eachk≥3, at least one off andf (k) has infinitely many non-real zeros. Together with a result of Edwards and Hellerstein, this establishes the analogue for higher derivatives of a conjecture going back to Wiman around 1911.
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Research partly carried out during a visit to the Christian-Albrechts-Universität Kiel, supported by a grant from the Alexander von Humboldt Stiftung. The author thanks the Mathematisches Seminar and in particular Walter Bergweiler for their hospitality.
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Langley, J.K. Non-real zeros of higher derivatives of real entire functions of infinite order. J. Anal. Math. 97, 357–396 (2005). https://doi.org/10.1007/BF02807411
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DOI: https://doi.org/10.1007/BF02807411