"숫자 12와 24"의 두 판 사이의 차이

수학노트
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63번째 줄: 63번째 줄:
 
** Bjorn Poonen and Fernando Rodriguez-Villegas
 
** Bjorn Poonen and Fernando Rodriguez-Villegas
 
** <cite>The American Mathematical Monthly</cite>, Vol. 107, No. 3 (Mar., 2000), pp. 238-250
 
** <cite>The American Mathematical Monthly</cite>, Vol. 107, No. 3 (Mar., 2000), pp. 238-250
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* [http://math.ucr.edu/home/baez/numbers/ My Favorite Numbers] : [http://math.ucr.edu/home/baez/numbers/#5 5], [http://math.ucr.edu/home/baez/numbers/#8 8], and [http://math.ucr.edu/home/baez/numbers/#24 24]<br>
 
* [http://math.ucr.edu/home/baez/numbers/ My Favorite Numbers] : [http://math.ucr.edu/home/baez/numbers/#5 5], [http://math.ucr.edu/home/baez/numbers/#8 8], and [http://math.ucr.edu/home/baez/numbers/#24 24]<br>
 
** John Baez
 
** John Baez
73번째 줄: 72번째 줄:
 
** W. S. Anglin
 
** W. S. Anglin
 
** <cite>The American Mathematical Monthly</cite>, Vol. 97, No. 2 (Feb., 1990), pp. 120-124
 
** <cite>The American Mathematical Monthly</cite>, Vol. 97, No. 2 (Feb., 1990), pp. 120-124
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* THE PICARD GROUP OF THE MODULI STACK OF ELLIPTIC CURVES
+
* This Week's Finds in Mathematical Physics (Week 125)<br>
 +
** John Baez
 +
** November 3, 1998
 +
* Picard Groups of Moduli Problems
 +
*  David Mumford<br> Arithmetical Algebraic Geometry, Proceedings of a Conference Held at Purdue University<br>

2009년 2월 4일 (수) 05:55 판

간단한 소개
  • 수학에서 숫자 12와 24는 매우 흥미로운 수.
  • modular group 과 깊게 관련되어 있음.
    • 12 = cusp form이 가질수 있는 가장 작은 weight
      \(\Delta(\tau)= q\prod_{n>0}(1-q^n)^{24}= q-24q+252q^2+\cdots\)
      는 weight 12 cusp form
    • \(SL(2,Z)_{ab}=C_{12}\)
    • \(\chi(SL(2,Z))=-\frac{1}{12}\)
  • 24
    • The Eisenstein series
      \(E_2=1+24\sum_{n=1}^{\infty}\sigma_1(n)q^n\)
       
    • Leech 격자의 차원
    • Sporadic group M24
    • If we take a double cover Mp2(Z) of SL2(Z), we have (Mp2(Z))ab = Z/24.
  • 26=24+2 is the critical dimension in bosonic string theory

 

하위주제들

 

관련된 학부 과목과 미리 알고 있으면 좋은 것들

 

 

관련된 대학원 과목

 

 

관련된 다른 주제들

 

표준적인 도서 및 추천도서

 

 

위키링크

 

참고할만한 자료
  • Lattice Polygons and the Number 12
    • Bjorn Poonen and Fernando Rodriguez-Villegas
    • The American Mathematical Monthly, Vol. 107, No. 3 (Mar., 2000), pp. 238-250
  • My Favorite Numbers : 5, 8, and 24
  • A short proof of the twelve-point theorem
    • Repovscaron D.; Skopenkov M.; Cencelj M.
    • Mathematical Notes, Volume 77, Number 1, January 2005 , pp. 108-111(4)
  • The Square Pyramid Puzzle
    • W. S. Anglin
    • The American Mathematical Monthly, Vol. 97, No. 2 (Feb., 1990), pp. 120-124
  • This Week's Finds in Mathematical Physics (Week 125)
    • John Baez
    • November 3, 1998
  • Picard Groups of Moduli Problems
  • David Mumford
    Arithmetical Algebraic Geometry, Proceedings of a Conference Held at Purdue University
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