TY - JOUR
T1 - Maximum and Average Valence of Meromorphic Functions
AU - Hinkkanen, Aimo
AU - Miles, Joseph
N1 - Publisher Copyright:
© The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2024.
PY - 2024/9
Y1 - 2024/9
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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U2 - 10.1007/s40315-024-00533-8
DO - 10.1007/s40315-024-00533-8
M3 - Article
AN - SCOPUS:85189018188
SN - 1617-9447
VL - 24
SP - 575
EP - 603
JO - Computational Methods and Function Theory
JF - Computational Methods and Function Theory
IS - 3
ER -