最終更新日：2024/08/07
(mathematics) A result on the class group of certain number fields, strengthening Ernst Kummer's theorem to the effect that the prime p divides the class number of the cyclotomic field of p-th roots of unity iff p divides the numerator of the n-th Bernoulli number Bₙ for some n, 0 < n < p − 1. The Herbrand–Ribet theorem specifies what, in particular, it means when p divides such an Bₙ.
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Herbrand-Ribet theorem
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Herbrand-Ribet theorem
name
(mathematics)
A
result
on
the
class
group
of
certain
number
fields,
strengthening
Ernst
Kummer's
theorem
to
the
effect
that
the
prime
p
divides
the
class
number
of
the
cyclotomic
field
of
p-th
roots
of
unity
iff
p
divides
the
numerator
of
the
n-th
Bernoulli
number
Bₙ
for
some
n,
0
<
n
<
p
−
1.
The
Herbrand–Ribet
theorem
specifies
what,
in
particular,
it
means
when
p
divides
such
an
Bₙ.
意味（1）
(mathematics)
A
result
on
the
class
group
of
certain
number
fields,
strengthening
Ernst
Kummer's
theorem
to
the
effect
that
the
prime
p
divides
the
class
number
of
the
cyclotomic
field
of
p-th
roots
of
unity
iff
p
divides
the
numerator
of
the
n-th
Bernoulli
number
Bₙ
for
some
n,
0
<
n
<
p
−
1.
The
Herbrand–Ribet
theorem
specifies
what,
in
particular,
it
means
when
p
divides
such
an
Bₙ.
