"타원곡선"의 두 판 사이의 차이
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| 22번째 줄: | 22번째 줄: | ||
* chord-tangent method | * chord-tangent method | ||
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| + | <h5>rank와 torsion</h5> | ||
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| 113번째 줄: | 121번째 줄: | ||
<h5 style="margin: 0px; line-height: 3.428em; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">관련도서 및 추천도서</h5> | <h5 style="margin: 0px; line-height: 3.428em; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">관련도서 및 추천도서</h5> | ||
| − | * | + | * [http://books.google.com/books?id=99v9XcOjhO4C&printsec=frontcover&dq=elliptic+curves&ei=cODSSvy2Coi0kASl5b2MDg Introduction to elliptic curves and modular forms]<br> |
** Neal Koblitz - 1993 | ** Neal Koblitz - 1993 | ||
* [http://books.google.com/books?id=mAJei2-JcE4C&printsec=frontcover&dq=rational+points+on+elliptic+curves&ei=3NfSSqfuKIGEkgTmqsgK&hl=ko#v=onepage&q=&f=false Rational points on elliptic curves]<br> | * [http://books.google.com/books?id=mAJei2-JcE4C&printsec=frontcover&dq=rational+points+on+elliptic+curves&ei=3NfSSqfuKIGEkgTmqsgK&hl=ko#v=onepage&q=&f=false Rational points on elliptic curves]<br> | ||
** Joseph H. Silverman, John Torrence Tate - 1992 | ** Joseph H. Silverman, John Torrence Tate - 1992 | ||
| + | ** 학부생의 입문용으로 좋은 책 | ||
* [http://books.google.com/books?hl=ko&lr=&id=Z90CA_EUCCkC&oi=fnd&pg=PR5&dq=%22Silverman%22+%22The+arithmetic+of+elliptic+curves%22+&ots=3K5hjqYj17&sig=zDmIXkvS7EaFwu4bnEbxmWUpFys#v=onepage&q=&f=false The Arithmetic of Elliptic Curves]<br> | * [http://books.google.com/books?hl=ko&lr=&id=Z90CA_EUCCkC&oi=fnd&pg=PR5&dq=%22Silverman%22+%22The+arithmetic+of+elliptic+curves%22+&ots=3K5hjqYj17&sig=zDmIXkvS7EaFwu4bnEbxmWUpFys#v=onepage&q=&f=false The Arithmetic of Elliptic Curves]<br> | ||
** Silverman, Joseph H. (1986), Graduate Texts in Mathematics, 106, Springer-Verlag<br> | ** Silverman, Joseph H. (1986), Graduate Texts in Mathematics, 106, Springer-Verlag<br> | ||
2009년 10월 13일 (화) 08:54 판
간단한 소개
격자와 타원곡선
\(y^2=4x^3-g_2(\tau)x-g_3\)
\(g_2(\tau) = 60G_4=60\sum_{ (m,n) \neq (0,0)} \frac{1}{(m+n\tau )^{4}}\)
\(g_3(\tau) = 140G_6=140\sum_{ (m,n) \neq (0,0)} \frac{1}{(m+n\tau )^{6}}\)
군의 구조
- chord-tangent method
rank와 torsion
예
\(y^2=x^3-x\)
[/pages/2061314/attachments/2299029 MSP1975197gdf732cih44i50000361d01gd578fhc4a.gif]
\(y^2=4x^3-4x\)
\(2\omega=4\int_0^1\frac{dx}{\sqrt{1-x^4}}=B(1/2,1/4)=\frac{\Gamma(\frac{1}{2})\Gamma(\frac{1}{4})}{\Gamma(\frac{3}{4})}=5.24\cdots\)
congruent number 문제
재미있는 사실
역사
관련된 다른 주제들
- 타원적분
- lemniscate 곡선의 길이와 타원적분
- 정수계수 이변수 이차형식(binary integral quadratic forms)
- j-invariant
- 아이젠슈타인 급수(Eisenstein series)
- 베타적분
- 사각 피라미드 퍼즐
수학용어번역
사전 형태의 자료
- http://ko.wikipedia.org/wiki/타원곡선
- http://en.wikipedia.org/wiki/elliptic_curve
- http://en.wikipedia.org/wiki/
- http://www.wolframalpha.com/input/?i=y^2=x^3-x
- http://www.wolframalpha.com/input/?i=
- NIST Digital Library of Mathematical Functions
관련논문
- Conics - a Poor Man's Elliptic Curves
- Franz Lemmermeyer, arXiv:math/0311306v1
- Elliptic Curves
- John Stillwell, The American Mathematical Monthly, Vol. 102, No. 9 (Nov., 1995), pp. 831-837
- Three Fermat Trails to Elliptic Curves
- Ezra Brown, The College Mathematics Journal, Vol. 31, No. 3 (May, 2000), pp. 162-172
- http://www.jstor.org/action/doBasicSearch?Query=elliptic+curves
- http://www.jstor.org/action/doBasicSearch?Query=congruent+number+problem
- http://www.jstor.org/action/doBasicSearch?Query=
관련도서 및 추천도서
- Introduction to elliptic curves and modular forms
- Neal Koblitz - 1993
- Rational points on elliptic curves
- Joseph H. Silverman, John Torrence Tate - 1992
- 학부생의 입문용으로 좋은 책
- The Arithmetic of Elliptic Curves
- Silverman, Joseph H. (1986), Graduate Texts in Mathematics, 106, Springer-Verlag
- Silverman, Joseph H. (1986), Graduate Texts in Mathematics, 106, Springer-Verlag
- 도서내검색
- 도서검색
관련기사
- 네이버 뉴스 검색 (키워드 수정)