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On deviations and spreads of entire curves

Volume 123 / 2019

Arnold Kowalski, Ivan Marchenko Annales Polonici Mathematici 123 (2019), 345-368 MSC: Primary 32H30, 30D35; Secondary 32A22, 30D30. DOI: 10.4064/ap180723-15-2 Published online: 29 July 2019


We consider the influence that the number of separated maximum points of entire curves has on their growth and value distribution. We give upper estimates of Petrenko’s deviation of entire curves in terms of the number of separated maximum points and sharp lower estimates of spread in terms of the number of maximum points, Nevanlinna’s defect and deviation. We also give examples showing that the estimates are sharp.


  • Arnold KowalskiSchool of Mathematics
    West Pomeranian University of Technology
    Al. Piastów 48
    70-311 Szczecin, Poland
  • Ivan MarchenkoFaculty of Mathematics and Physics
    University of Szczecin
    Wielkopolska 15
    70-451 Szczecin, Poland

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