On the maximum modulus of a complex polynomial
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Date
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Ankara Üniversitesi
Abstract
In this paper we impose distinct restrictions on the moduli of the zeros of
p
(
z
)
=
n
∑
v
=
0
a
v
z
v
and investigate the dependence of
∥
p
(
R
z
)
−
p
(
σ
z
)
∥
,
R
>
σ
≥
1
on
M
α
and
M
α
+
π
, where
M
α
=
max
1
≤
k
≤
n
|
p
(
e
i
(
α
+
2
k
π
)
/
n
)
|
and on certain coefficients of
p
(
z
)
. This paper comprises several results, which in particular yields some classical polynomial inequalities as special cases. Moreover, the problem of estimating
p
(
1
−
w
n
)
,
0
<
w
≤
given
p
(
1
)
=
0
is considered.