"숫자 12와 24"의 두 판 사이의 차이

2009년 2월 3일 (화) 10:56 판

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
26= Critical dimension in bosonic string theory
25−1 = 24 is related to:
1. D(t) = h(t)24, where D is the discriminant cusp form of weight 12, and h is the
Dedekind function.
2. The constant term of j(t)−720 = q−1 +24+196884q+. . . , which is the “right
normalization” of this modular function.
3. The Eisenstein series E2 = 1−24ås1(n)qn.
4. Dimension of the Leech Lattice.
5. Sporadic group M24
6. If we take a double cover Mp2(Z) of SL2(Z), we have (Mp2(Z))ab = Z/24.

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
- John Baez
- The Rankin Lectures, University of Glasgow, September 15-19, 2008
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

@@ 4번째 줄: / 4번째 줄: @@
 *  modular group 과 깊게 관련되어 있음.<br>
 **  12 = cusp form이 가질수 있는 가장 작은 weight<br><math>\Delta(\tau)= q\prod_{n>0}(1-q^n)^{24}= q-24q+252q^2+\cdots</math><br> 는 weight 12 cusp form<br>
-*
+* 26= Critical dimension in bosonic string theory<br> 25−1 = 24 is related to:<br> 1. D(t) = h(t)24, where D is the discriminant cusp form of weight 12, and h is the<br> Dedekind function.<br> 2. The constant term of j(t)−720 = q−1 +24+196884q+. . . , which is the “right<br> normalization” of this modular function.<br> 3. The Eisenstein series E2 = 1−24ås1(n)qn.<br> 4. Dimension of the Leech Lattice.<br> 5. Sporadic group M24<br> 6. If we take a double cover Mp2(Z) of SL2(Z), we have (Mp2(Z))ab = Z/24.