Last Updated
：2025/11/22
Riemann zeta function
Noun
uncountable
usually
countable
(number
theory,
analytic
number
theory,
uncountable)
The
function
ζ
defined
by
the
Dirichlet
series
𝜁(s)=∑ₙ₌₁ ᪲1/(nˢ)=1/(1ˢ)+1/(2ˢ)+1/(3ˢ)+1/(4ˢ)+⋯,
which
is
summable
for
points
s
in
the
complex
half-plane
with
real
part
>
1;
the
analytic
continuation
of
said
function,
being
a
holomorphic
function
defined
on
the
complex
numbers
with
pole
at
1.
Japanese Meaning
リーマンゼータ関数（ζ関数）は、ディリクレ級数 ζ(s)=∑ₙ₌₁ 1/(n^s) により定義され、実部が1より大きい複素数 s の半平面で収束する関数です。解析接続により、この関数は複素全体に拡張され、1に極を持つホロモルフィック関数（複素解析可能な関数）として扱われ、数論および解析数論で重要な役割を果たします。
Sense（1）
(number
theory,
analytic
number
theory,
uncountable)
The
function
ζ
defined
by
the
Dirichlet
series
𝜁(s)=∑ₙ₌₁ ᪲1/(nˢ)=1/(1ˢ)+1/(2ˢ)+1/(3ˢ)+1/(4ˢ)+⋯,
which
is
summable
for
points
s
in
the
complex
half-plane
with
real
part
>
1;
the
analytic
continuation
of
said
function,
being
a
holomorphic
function
defined
on
the
complex
numbers
with
pole
at
1.
（ plural ）
Quizzes for review
(number theory, analytic number theory, uncountable) The function ζ defined by the Dirichlet series 𝜁(s)=∑ₙ₌₁ ᪲1/(nˢ)=1/(1ˢ)+1/(2ˢ)+1/(3ˢ)+1/(4ˢ)+⋯, which is summable for points s in the complex half-plane with real part > 1; the analytic continuation of said function, being a holomorphic function defined on the complex numbers with pole at 1.
音声機能が動作しない場合はこちらをご確認ください
See correct answer
Riemann zeta function
Research in analytic number theory often revolves around the Riemann zeta function and its complex zeros.
See correct answer
Research in analytic number theory often revolves around the Riemann zeta function and its complex zeros.
音声機能が動作しない場合はこちらをご確認ください
English - English
Word Edit Setting
- Users who have edit permission for words - All Users
- Screen new word creation
- Screen word edits
- Screen word deletion
- Screen the creation of new headword that may be duplicates
- Screen changing entry name
- Users authorized to vote on judging - Editor
- Number of votes required for decision - 1
Sentence Edit Setting
- Users who have edit permission for sentences - All Users
- Screen sentence deletion
- Users authorized to vote on judging - Editor
- Number of votes required for decision - 1
Quiz Edit Setting
- Users who have edit permission for quizzes - All Users
- Users authorized to vote on judging - Editor
- Number of votes required for decision - 1
