Journal d’Analyse Mathematique

, Volume 62, Issue 1, pp 271–286 | Cite as

On the zeros of meromorphic functions of the formf(z)=Σ k=1 a k/zz k

  • Alexandre Eremenko
  • Jim Langley
  • John Rossi


We study the zero distribution of meromorphic functions of the formf(z)=Σ k=1 a k/zz k wherea k >0. Noting thatf is the complex conjugate of the gradient of a logarithmic potential, our results have application in the study of the equilibrium points of such a potential.

Furthermore, answering a question of Hayman, we also show that the derivative of a meromorphic function of order at most one, minimal type has infinitely many zeros.


Entire Function Meromorphic Function Straight Line Segment Subharmonic Function Level Curf 
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Copyright information

© Hebrew University 1994

Authors and Affiliations

  • Alexandre Eremenko
    • 1
  • Jim Langley
    • 2
  • John Rossi
    • 3
  1. 1.Department of MathematicsPuruue UniversityLafayetteUSA
  2. 2.Department of MathematicsUniversity of NottinghamEngland
  3. 3.Department of MathematicsVirginia Polytechnic Institute and State UniversityBlacksburgUSA

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