"3-manifolds and their invariants"의 두 판 사이의 차이

2010년 3월 31일 (수) 14:18 판

Dedekind zeta funciton evaluated at 2 gives a number related to volume of 3-manifold
Bloch-Wigner dilogarithm is involved

Prove
\(\frac{24}{7\sqrt{7}}\int_{\pi/3}^{\pi/2}\ln|\frac{\tan t+\sqrt{7}}{\tan t-\sqrt{7}}|\,dt=\frac{2}{\sqrt{7}}(D(e^{2\pi i/7})+D(e^{4\pi i/7})-D(e^{6\pi i/7}))=\frac{2}{\sqrt{7}}(Cl(2\pi /7})+Cl(4\pi/7})-Cl(6\pi/7}))\)
an open problem in integration

[[4909919|]]

@@ 41번째 줄: / 41번째 줄: @@
 * http://www.google.com/search?hl=en&tbs=tl:1&q=
+==== 하위페이지 ====
+* [[threefolds and their invariants|hyperbolic 3-manifold]]<br>
+** [[Chern-Simons gauge theory and invariant|Chern-Simons invariant]]<br>
+** [[Kashaev's volume conjecture|Kashaev's volume Conjecture]]<br>
+** [[triangulations and Bloch group]]<br>
+** [[volume of hyperbolic threefolds and L-values|volume of hyperbolic 3-manifolds and L-values]]<br>
@@ 54번째 줄: / 70번째 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%;">encyclopedia</h5>
-* http://ko.wikipedia.org/wiki/
+*   <br>
-* [http://en.wikipedia.org/wiki/Figure-eight_knot_%28mathematics%29 http://en.wikipedia.org/wiki/Figure-eight_knot_(mathematics)]
+* http://ko.wikipedia.org/wiki/[http://en.wikipedia.org/wiki/Figure-eight_knot_%28mathematics%29 ]
 * http://en.wikipedia.org/wiki/
 * Princeton companion to mathematics([[2910610/attachments/2250873|Companion_to_Mathematics.pdf]])