"데데킨트 에타함수"의 두 판 사이의 차이

2009년 8월 17일 (월) 18:06 판

\(\eta(\tau) = q^{1/24} \prod_{n=1}^{\infty} (1-q^{n})\)

\(\eta(-\frac{1}{\tau}) =\sqrt{\frac{\tau}{i}}\eta(\tau)\)

\(\Delta(\tau)=\eta(\tau)^{24}= q\prod_{n>0}(1-q^n)^{24}=q-24q+252q^2+\cdots\)

@@ 11번째 줄: / 11번째 줄: @@
 <math>\eta(-\frac{1}{\tau}) =\sqrt{\frac{\tau}{i}}\eta(\tau)</math>
+* 에타함수의 24제곱은 weight 12인 cusp 형식이 되므로, discriminant 함수가 된다
+<math>\Delta(\tau)=\eta(\tau)^{24}= q\prod_{n>0}(1-q^n)^{24}=q-24q+252q^2+\cdots</math>
@@ 76번째 줄: / 78번째 줄: @@
 <h5>참고할만한 자료</h5>
+* [http://projecteuclid.org/DPubS?verb=Display&version=1.0&service=UI&handle=euclid.bams/1183533964&page=record Missed opportunities]<br>
+** Freeman J. Dyson, Bull. Amer. Math. Soc. Volume 78, Number 5 (1972), 635-652.
 * http://ko.wikipedia.org/wiki/
 * http://en.wikipedia.org/wiki/Dedekind_eta_function
-* http://viswiki.com/en/
-* http://front.math.ucdavis.edu/search?a=&t=&c=&n=40&s=Listings&q=
-* http://www.ams.org/mathscinet/search/publications.html?pg4=AUCN&s4=&co4=AND&pg5=TI&s5=&co5=AND&pg6=PC&s6=&co6=AND&pg7=ALLF&co7=AND&Submit=Search&dr=all&yrop=eq&arg3=&yearRangeFirst=&yearRangeSecond=&pg8=ET&s8=All&s7=
-* 다음백과사전 http://enc.daum.net/dic100/search.do?q=
-* [http://mathnet.kaist.ac.kr/mathnet/math_list.php?mode=list&ftype=&fstr= 대한수학회 수학 학술 용어집]