Maximum and Average Valence of Meromorphic Functions

Aimo Hinkkanen, Joseph Miles

Research output: Contribution to journalArticlepeer-review


If f is a meromorphic function from the complex plane C to the extended complex plane C¯, for r>0 let n(r) be the maximum number of solutions in {z:|z|≤r} of f(z)=a for a∈C¯, and let A(r, f) be the average number of such solutions. Using a technique introduced by Toppila, we exhibit a meromorphic function for which lim infr→∞n(r)/A(r,f)≥1.07328.

Original languageEnglish (US)
JournalComputational Methods and Function Theory
StateAccepted/In press - 2024


  • Meromorphic functions
  • Nevanlinna theory
  • Primary 30D35
  • Value distribution

ASJC Scopus subject areas

  • Analysis
  • Computational Theory and Mathematics
  • Applied Mathematics


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