Shared values for differences and Borel exceptional values

✍ Scribed by Chen, Chuang-Xin; Chen, Zong-Xuan

• Book ID: 121700650
• Publisher: Walter de Gruyter GmbH & Co. KG
• Year: 2014
• Tongue: English
• Weight: 460 KB
• Volume: 21
• Category: Article
• ISSN: 1072-947X
• DOI: 10.1515/gmj-2014-0012

✦ Synopsis

Abstract.

In this paper, we prove that if f is a transcendental
meromorphic function of finite order which has two Borel
exceptional values a (

∈
ℂ

$\in \mathbb {C}$

) and b (

∈
ℂ
∪
{
∞
}

$\in \mathbb {C}\cup \lbrace \infty \rbrace $

),
and if

f
(
z
+
η
)

f
(
z
)

$f(z+\eta )-f(z)$

and

f
(
z
)

$f(z)$

share values d (

d
∈
ℂ

$d\in \mathbb {C}$

and

d
≠
a

$d\ne a$

),
b CM,

f
(
z
)

$f(z)$

is not periodic of period

η

$\eta $

(

∈
ℂ

$\in \mathbb {C}$

), then

b

∞

$b=\infty $

,

d
≠

a
2

,
0

$d\ne \frac{a}{2},0$

and

f

(
z
)

=
a
+
c

e

c
1

z

$f(z)=a+ce^{c_1z}$

,
where

c
,

c
1

$c,c_1$

are two nonzero constants.