"데데킨트 합"의 두 판 사이의 차이
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| 55번째 줄: | 55번째 줄: | ||
<h5 style="line-height: 3.428em; margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic', dotum, gulim, sans-serif; font-size: 1.166em; background-image: ; background-color: initial; background-position: 0px 100%;">관련도서 및 추천도서</h5> | <h5 style="line-height: 3.428em; margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic', dotum, gulim, sans-serif; font-size: 1.166em; background-image: ; background-color: initial; background-position: 0px 100%;">관련도서 및 추천도서</h5> | ||
| + | * [http://math.sfsu.edu/beck/ccd.html Computing the Continuous Discretely: Integer-Point Enumeration in Polyhedra]<br> | ||
| + | ** Matthias Beck and Sinai Robins, Springer, 2007<br> | ||
* Dedekind Sums, The Carus Mathematical Monographs<br> | * Dedekind Sums, The Carus Mathematical Monographs<br> | ||
** H. Rademacher and E. Grosswald<br> | ** H. Rademacher and E. Grosswald<br> | ||
| 77번째 줄: | 79번째 줄: | ||
<h5 style="line-height: 3.428em; margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic', dotum, gulim, sans-serif; font-size: 1.166em; background-image: ; background-color: initial; background-position: 0px 100%;">참고할만한 자료</h5> | <h5 style="line-height: 3.428em; margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic', dotum, gulim, sans-serif; font-size: 1.166em; background-image: ; background-color: initial; background-position: 0px 100%;">참고할만한 자료</h5> | ||
| + | |||
| + | * [http://arxiv.org/abs/math.NT/0112077 Dedekind cotangent sums]<br> | ||
| + | ** Matthias Beck, Acta Arithmetica 109, no.2 (2003), 109-130 | ||
* [http://www.jstor.org/stable/2316571?&Search=yes&term=Emil&term=Grosswald,&term=,&term="Dedekind-Rademacher+sums"&list=hide&searchUri=/action/doBasicSearch%3FQuery%3DEmil%2BGrosswald%252C%2B%2522%2BDedekind-Rademacher%2Bsums%2B%2522%252C%26x%3D0%26y%3D0%26wc%3Don&item=1&ttl=3&returnArticleService=showArticle Dedekind-Rademacher Sums]<br> | * [http://www.jstor.org/stable/2316571?&Search=yes&term=Emil&term=Grosswald,&term=,&term="Dedekind-Rademacher+sums"&list=hide&searchUri=/action/doBasicSearch%3FQuery%3DEmil%2BGrosswald%252C%2B%2522%2BDedekind-Rademacher%2Bsums%2B%2522%252C%26x%3D0%26y%3D0%26wc%3Don&item=1&ttl=3&returnArticleService=showArticle Dedekind-Rademacher Sums]<br> | ||
** Emil Grosswald, The American Mathematical Monthly, Vol. 78, No. 6 (Jun. - Jul., 1971), pp. 639-644 | ** Emil Grosswald, The American Mathematical Monthly, Vol. 78, No. 6 (Jun. - Jul., 1971), pp. 639-644 | ||
| − | * | + | * [http://projecteuclid.org/DPubS?verb=Display&version=1.0&service=UI&handle=euclid.nmj/1118797877&page=record The reciprocity of Dedekind sums and the factor set for the universal covering group of] <math>{\rm SL}(2,\,R)</math><br> |
| − | ** | + | ** Tetsuya Asai, Source: Nagoya Math. J. Volume 37 (1970), 67-80. |
* http://ko.wikipedia.org/wiki/ | * http://ko.wikipedia.org/wiki/ | ||
* http://en.wikipedia.org/wiki/Dedekind_sum | * http://en.wikipedia.org/wiki/Dedekind_sum | ||
2009년 8월 18일 (화) 05:16 판
간단한 소개
- 다음과 같이 sawtooth 함수를 정의하자
\(\left((x)\right)= \begin{cases} x-\lfloor x\rfloor - 1/2 & \mbox{ if }x\in\mathbb{R}\setminus\mathbb{Z} \\ 0 & \mbox{ if } x\in\mathbb{Z} \end{cases}\)
[/pages/3985465/attachments/1997179 Discontinuous-function-and-Fourier.gif]
- 서로 소인 두 정수 \(h, k>0\)에 대하여 데데킨트 합 \(s(h,k)\)은 다음과 같이 정의됨
\(s(h,k)=\sum_{n\mod k} \left( \left( \frac{n}{k} \right) \right) \left( \left( \frac{hn}{k} \right) \right)\)
상호법칙
(정리) 데데킨트
서로 소인 양의 정수 \(b\)와 \(c\)에 대하여 다음이 성립한다.
\(s(b,c)+s(c,b) =\frac{1}{12}\left(\frac{b}{c}+\frac{1}{bc}+\frac{c}{b}\right)-\frac{1}{4}\)
일반화
\(D(a,b;c)=\sum_{n\mod c} \left( \left( \frac{an}{c} \right) \right) \left( \left( \frac{bn}{c} \right) \right)\)
상위 주제
재미있는 사실
역사
관련된 다른 주제들
관련도서 및 추천도서
- Computing the Continuous Discretely: Integer-Point Enumeration in Polyhedra
- Matthias Beck and Sinai Robins, Springer, 2007
- Matthias Beck and Sinai Robins, Springer, 2007
- Dedekind Sums, The Carus Mathematical Monographs
- H. Rademacher and E. Grosswald
- H. Rademacher and E. Grosswald
- 도서내검색
- 도서검색
수학용어번역
참고할만한 자료
- Dedekind cotangent sums
- Matthias Beck, Acta Arithmetica 109, no.2 (2003), 109-130
- "Dedekind-Rademacher+sums"&list=hide&searchUri=/action/doBasicSearch%3FQuery%3DEmil%2BGrosswald%252C%2B%2522%2BDedekind-Rademacher%2Bsums%2B%2522%252C%26x%3D0%26y%3D0%26wc%3Don&item=1&ttl=3&returnArticleService=showArticle Dedekind-Rademacher Sums
- Emil Grosswald, The American Mathematical Monthly, Vol. 78, No. 6 (Jun. - Jul., 1971), pp. 639-644
- The reciprocity of Dedekind sums and the factor set for the universal covering group of \({\rm SL}(2,\,R)\)
- Tetsuya Asai, Source: Nagoya Math. J. Volume 37 (1970), 67-80.
- http://ko.wikipedia.org/wiki/
- http://en.wikipedia.org/wiki/Dedekind_sum
- http://www.wolframalpha.com/input/?i=sawtooth+function
- 네이버 오늘의과학
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