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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
Article

Abstract

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.

Keywords

Entire Function Meromorphic Function Straight Line Segment Subharmonic Function Level Curf 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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