타원곡선

 

 

격자와 타원곡

\(y^2=4x^3-g_2(\tau)x-g_3\)

\(g_2(\tau) = 60G_4=60\sum_{ (m,n) \neq (0,0)} \frac{1}{(m+n\tau )^{4}}\)

\(g_3(\tau) = 140G_6=140\sum_{ (m,n) \neq (0,0)} \frac{1}{(m+n\tau )^{6}}\)

• 아이젠슈타인 급수(Eisenstein series)
  

 

 

군의 구조

• chord-tangent method

 

 

예

\(y^2=x^3-x\)

[/pages/2061314/attachments/2299029 MSP1975197gdf732cih44i50000361d01gd578fhc4a.gif]

\(y^2=4x^3-4x\)

\(2\omega=4\int_0^1\frac{dx}{\sqrt{1-x^4}}=B(1/2,1/4)=\frac{\Gamma(\frac{1}{2})\Gamma(\frac{1}{4})}{\Gamma(\frac{3}{4})}=5.24\cdots\)

 

 

 

 

 

 

역사

• 수학사연표

 

 

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

• 대한수학회 수학 학술 용어집
  
  • http://mathnet.kaist.ac.kr/mathnet/math_list.php?mode=list&ftype=eng_term&fstr=
• 대한수학회 수학용어한글화 게시판

 

 

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=

 

 

관련도서 및 추천도서

• Rational points on elliptic curves‎
  
  • Joseph H. Silverman, John Torrence Tate - 1992
• The Arithmetic of Elliptic Curves
  
  • Silverman, Joseph H. (1986), Graduate Texts in Mathematics, 106, Springer-Verlag
    
• 도서내검색
  
  • http://books.google.com/books?q=
  • http://book.daum.net/search/contentSearch.do?query=타원곡선
  • http://book.daum.net/search/contentSearch.do?query=
• 도서검색
  
  • http://books.google.com/books?q=elliptic+curves
  • http://books.google.com/books?q=
  • http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=
  • http://book.daum.net/search/mainSearch.do?query=

 

 

관련기사

• 네이버 뉴스 검색 (키워드 수정)
  
  • http://news.search.naver.com/search.naver?where=news&x=0&y=0&sm=tab_hty&query=타원곡선
  • http://news.search.naver.com/search.naver?where=news&x=0&y=0&sm=tab_hty&query=
  • http://news.search.naver.com/search.naver?where=news&x=0&y=0&sm=tab_hty&query=

 

 

블로그

• 구글 블로그 검색 http://blogsearch.google.com/blogsearch?q=
• 네이버 오늘의과학