Finiteness of meromorphic functions on an annulus sharing four values regardless of multiplicity

Si, Duc Quang, and Tran, An Hai. "Finiteness of meromorphic functions on an annulus sharing four values regardless of multiplicity." Mathematica Bohemica 145.2 (2020): 163-176. <http://eudml.org/doc/297365>.

@article{Si2020,
abstract = {This paper deals with the finiteness problem of meromorphic funtions on an annulus sharing four values regardless of multiplicity. We prove that if three admissible meromorphic functions $f_1$, $f_2$, $f_3$ on an annulus $\mathbb \{A\}(\{R_0\})$ share four distinct values regardless of multiplicity and have the complete identity set of positive counting function, then $f_1=f_2$ or $f_2=f_3$ or $f_3=f_1$. This result deduces that there are at most two admissible meromorphic functions on an annulus sharing a value with multiplicity truncated to level $2$ and sharing other three values regardless of multiplicity. This result also implies that there are at most three admissible meromorphic functions on an annulus sharing four values regardless of multiplicities. These results are a generalization and improvement of the previous results on finiteness problem of meromorphic functions on $\mathbb \{C\}$ sharing four values.},
author = {Si, Duc Quang, Tran, An Hai},
journal = {Mathematica Bohemica},
keywords = {meromorphic function; Nevanlinna theory; annulus},
language = {eng},
number = {2},
pages = {163-176},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Finiteness of meromorphic functions on an annulus sharing four values regardless of multiplicity},
url = {http://eudml.org/doc/297365},
volume = {145},
year = {2020},
}

TY - JOUR
AU - Si, Duc Quang
AU - Tran, An Hai
TI - Finiteness of meromorphic functions on an annulus sharing four values regardless of multiplicity
JO - Mathematica Bohemica
PY - 2020
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 145
IS - 2
SP - 163
EP - 176
AB - This paper deals with the finiteness problem of meromorphic funtions on an annulus sharing four values regardless of multiplicity. We prove that if three admissible meromorphic functions $f_1$, $f_2$, $f_3$ on an annulus $\mathbb {A}({R_0})$ share four distinct values regardless of multiplicity and have the complete identity set of positive counting function, then $f_1=f_2$ or $f_2=f_3$ or $f_3=f_1$. This result deduces that there are at most two admissible meromorphic functions on an annulus sharing a value with multiplicity truncated to level $2$ and sharing other three values regardless of multiplicity. This result also implies that there are at most three admissible meromorphic functions on an annulus sharing four values regardless of multiplicities. These results are a generalization and improvement of the previous results on finiteness problem of meromorphic functions on $\mathbb {C}$ sharing four values.
LA - eng
KW - meromorphic function; Nevanlinna theory; annulus
UR - http://eudml.org/doc/297365
ER -