Abstract
Abstract
In this paper, we discuss the unicity problem of certain shift polynomials. Suppose that cj
(j = 1, …, s) be distinct complex numbers, n, m, s and μj
(j = 1, …, s) are integers satisfying n + m > 4σ + 14, where σ = μ
1 + μ
2 + … μs
. We prove that if
p
n
(
γ
)
(
p
(
γ
)
−
1
)
m
∏
j
=
1
s
p
(
γ
+
c
j
)
μ
j
and
q
n
(
γ
)
(
q
(
γ
)
−
1
)
m
∏
j
=
1
s
q
(
γ
+
c
j
)
μ
j
share ″(α(γ),0)″, then either
p
(
γ
)
≡
q
(
γ
)
or
p
n
(
p
−
1
)
m
∏
j
=
1
s
p
(
γ
+
c
j
)
μ
j
−
q
n
(
q
−
1
)
m
∏
j
=
1
s
q
(
γ
+
c
j
)
μ
j
. The results obtained greatly improve the results of Saha (Korean J. Math. 28(4)(2020)) and C. Meng (Mathematica Bohemica 139(2014)).
Subject
General Physics and Astronomy
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