Maximum and Average Valence of Meromorphic Functions

Aimo Hinkkanen; Joseph Miles

doi:10.1007/s40315-024-00533-8

Maximum and Average Valence of Meromorphic Functions

Aimo Hinkkanen
, Joseph Miles

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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 inf_r→∞n(r)/A(r,f)≥1.07328.

Original language	English (US)
Pages (from-to)	575-603
Number of pages	29
Journal	Computational Methods and Function Theory
Volume	24
Issue number	3
Early online date	Mar 30 2024
DOIs	https://doi.org/10.1007/s40315-024-00533-8
State	Published - Sep 2024

Keywords

Meromorphic functions
Nevanlinna theory
Primary 30D35
Value distribution

ASJC Scopus subject areas

Analysis
Computational Theory and Mathematics
Applied Mathematics

Online availability

10.1007/s40315-024-00533-8

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N2 - 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.

AB - 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.

KW - Meromorphic functions

KW - Nevanlinna theory

KW - Primary 30D35

KW - Value distribution

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ER -

Maximum and Average Valence of Meromorphic Functions

Abstract

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