Last Updated
：2025/12/08
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.
Quizzes for review
(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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See correct answer
Sendov's conjecture
Although many partial results are known for specific degrees, Sendov's conjecture remains one of the most intriguing open problems in complex polynomial theory.
See correct answer
Although many partial results are known for specific degrees, Sendov's conjecture remains one of the most intriguing open problems in complex polynomial theory.
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