"Zeta value at 2"의 두 판 사이의 차이

2012년 8월 26일 (일) 19:07 판

복소이차수체의 데데킨트 제테함수

항목으로 옮겨짐

@@ 1번째 줄: / 1번째 줄: @@
-<h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">introduction</h5>
+[http://pythagoras0.springnote.com/pages/11964298 복소이차수체의 데데킨트 제테함수]
-*  복소이차수체의 [http://pythagoras0.springnote.com/pages/4533335 데데킨트 제타함수]<br><math>\zeta_{K}(2)=\frac{\pi^2}{6\sqrt{|d_K|}}\sum_{(a,d_k)=1} (\frac{d_K}{a})D(e^{2\pi ia/|d_k|})</math><br>
+항목으로 옮겨짐
-*  Note that<br>
-**  the Clausen function and the Bloch-Wigner dilogarithms are same if <math>z=e^{i\theta}</math><br><math>\operatorname{Cl}_2(\theta)=-\int_0^{\theta} \ln |2\sin \frac{t}{2}| \,dt=\sum_{n=1}^{\infty}\frac{\sin (n\theta)}{n^2}</math><br><math>D(z)=\text{Im}(\operatorname{Li}_2(z))+\log|z|\arg(1-z)</math><br>
-<h5 style="line-height: 2em; margin: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">a few examples</h5>
-* http://books.google.co.kr/books?id=yrmT56mpw3kC&pg=PA367&dq=smallest+norms+of+prime+ideals&hl=ko&ei=IMRTTIaRGoqWvAP88MUZ&sa=X&oi=book_result&ct=result&resnum=4&ved=0CDgQ6AEwAw#v=onepage&q=smallest%20norms%20of%20prime%20ideals&f=false<br>
-<math>\zeta_{\mathbb{Q}\sqrt{-1}}(2)=1.50670301</math>
-<math>\zeta_{\mathbb{Q}\sqrt{-2}}(2)=1.75141751\cdots</math>
-<math>\zeta_{\mathbb{Q}\sqrt{-3}}(2)=\frac{\pi^2}{6\sqrt{3}}(D(e^{2\pi i/3})-D(e^{4\pi i/3}))=\frac{\pi^2}{3\sqrt{3}}D(e^{2\pi i/3})=1.285190955484149\cdots</math>
-<math>\zeta_{\mathbb{Q}\sqrt{-7}}(2)=\frac{\pi^2}{3\sqrt{7}}(D(e^{2\pi i/7})+D(e^{4\pi i/7})-D(e^{6\pi i/7}))=1.89484145</math>
-<math>\zeta_{\mathbb{Q}\sqrt{-11}}(2)=1.49613186</math>
-#  Cl[x_] := Im[PolyLog[2, Exp[I*x]]]<br> disc[n_] := NumberFieldDiscriminant[Sqrt[-n]]<br> L2[n_] :=<br>  1/Sqrt[Abs[disc[n]]]*<br>   Sum[JacobiSymbol[disc[n], k] Cl[2 Pi*k/Abs[disc[n]]], {k, 1,<br>     Abs[disc[n]] - 1}]<br> Zeta2[n_] := L2[n]*Pi^2/6<br> Zeta2[1]<br>
-<h5 style="line-height: 2em; margin: 0px;">figure eight knot complement</h5>
-<math>V=\frac{9\sqrt{3}}{\pi^2}\zeta_{\mathbb{Q}(\sqrt{-3})}(2)=3D(e^{\frac{2i\pi}{3}})=2D(e^{\frac{i\pi}{3}})=2.029883212819\cdots</math>
-<math>\zeta_{\mathbb{Q}(\sqrt{-3})}(2)=\frac{\pi^2}{3\sqrt{3}}D(e^{\frac{2\pi i}{3}})</math>
-<math>L_{-3}(2)=\frac{2}{\sqrt{3}}D(e^{\frac{2\pi  i}{3}})</math>
-*  2.02988321281930725<br><math>V(4_{1})=\frac{9\sqrt{3}}{\pi^2}\zeta_{\mathbb{Q}(\sqrt{-3})}(2)=3D(e^{\frac{2i\pi}{3}})=2D(e^{\frac{i\pi}{3}})=2.029883212819\cdots</math><br> where D is [http://pythagoras0.springnote.com/pages/4633853 Bloch-Wigner dilogarithm].<br>
-*  what is <math>\zeta_{\mathbb{Q}(\sqrt{-3})}(2)</math>? numerically 1.285190955484149<br>
-<h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">history</h5>
-* http://www.google.com/search?hl=en&tbs=tl:1&q=

"Zeta value at 2"의 두 판 사이의 차이

2012년 8월 26일 (일) 19:07 판

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