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On the number of solutions of some transcendental equations

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Abstract

We give upper and lower bounds for the number of solutions of the equation \(p(z)\log |z|+q(z)=0\) with polynomials p and q.

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Acknowledgements

We thank the referee for helpful suggestions.

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Authors and Affiliations

  1. Mathematisches Seminar, Christian-Albrechts-Universität zu Kiel, Ludewig-Meyn-Str. 4, 24098, Kiel, Germany

    Walter Bergweiler

  2. Department of Mathematics, Purdue University, West Lafayette, IN, 47907, USA

    Alexandre Eremenko

Authors
  1. Walter Bergweiler
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  2. Alexandre Eremenko
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Correspondence to Alexandre Eremenko.

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The authors declare that they have no conflict of interest.

Additional information

Dedicated to Dima Khavinson on the occasion of his 60th birthday.

Supported by NSF Grant DMS-1665115.

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Bergweiler, W., Eremenko, A. On the number of solutions of some transcendental equations. Anal.Math.Phys. 8, 185–196 (2018). https://doi.org/10.1007/s13324-017-0204-6

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  • DOI: https://doi.org/10.1007/s13324-017-0204-6

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