Abstract
AbstractIn this paper, we give the characteristic estimation of a meromorphic function f with the differential polynomials $f^{l}(f^{(k)})^{n}$
f
l
(
f
(
k
)
)
n
and obtain that $$\begin{aligned} T(r,f)\leq M\overline{N} \biggl(r,\frac{1}{f^{l}(f^{(k)})^{n}-a} \biggr)+S(r,f) \end{aligned}$$
T
(
r
,
f
)
≤
M
N
‾
(
r
,
1
f
l
(
f
(
k
)
)
n
−
a
)
+
S
(
r
,
f
)
holds for $M=\min \{\frac{1}{l-2},6\}$
M
=
min
{
1
l
−
2
,
6
}
, integers $l(\geq 2)$
l
(
≥
2
)
, $n(\geq 1)$
n
(
≥
1
)
, $k(\geq 1)$
k
(
≥
1
)
, and a non-zero constant a. This quantitative estimate is an interesting and complete extension of earlier results. The value distribution of a differential monomial of meromorphic functions is also investigated.
Funder
national outstanding youth science fund project of national natural science foundation of china
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis
Cited by
1 articles.
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