Last Updated：2024/08/08
(mathematics) A conjecture concerning the relationship between the locations of roots and critical points of a polynomial function of a complex variable. It states that for a polynomial f(z)=(z-r_1)⋯(z-r_n), qquad (n>2) with all roots r₁, ..., rₙ inside the closed unit disk |z| ≤ 1, each of the n roots is at a distance no more than 1 from at least one critical point.
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Sendov's conjecture
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Source Word
Sendov's conjecture
Proper noun
(mathematics)
A
conjecture
concerning
the
relationship
between
the
locations
of
roots
and
critical
points
of
a
polynomial
function
of
a
complex
variable.
It
states
that
for
a
polynomial
f(z)=(z-r_1)⋯(z-r_n),
qquad
(n>2)
with
all
roots
r₁,
...,
rₙ
inside
the
closed
unit
disk
|z|
≤
1,
each
of
the
n
roots
is
at
a
distance
no
more
than
1
from
at
least
one
critical
point.
Japanese Meaning
数学における予想。複素数変数の多項式 f(z) = (z - r₁)⋯(z - rₙ) (ただし n > 2) の全ての根 r₁, ..., rₙ が閉単位円 |z| ≤ 1 内に存在する場合、各根から1以内の距離に少なくとも一つの臨界点（導関数の根）が存在するという主張。
Sense（1）
(mathematics)
A
conjecture
concerning
the
relationship
between
the
locations
of
roots
and
critical
points
of
a
polynomial
function
of
a
complex
variable.
It
states
that
for
a
polynomial
f(z)=(z-r_1)⋯(z-r_n),
qquad
(n>2)
with
all
roots
r₁,
...,
rₙ
inside
the
closed
unit
disk
|z|
≤
1,
each
of
the
n
roots
is
at
a
distance
no
more
than
1
from
at
least
one
critical
point.
