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

2010년 3월 31일 (수) 04:52 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|]]

Determinations of rational Dedekind-zeta invariants of hyperbolic manifolds and Feynman knots and links
- J.M. Borwein, D.J. Broadhurst, 1998
Hyperbolic manifolds and special values of Dedekind zeta-functions
- Don Zagier, Inventiones Mathematicae, Volume 83, Number 2 / 1986년 6월
Commensurability classes and volumes of hyperbolic 3-manifolds
- A. Borel, Ann. Sc. Norm. Super. Pisa8, 1–33 (1981)

@@ 82번째 줄: / 82번째 줄: @@
 * [http://arxiv.org/abs/hep-th/9811173 Determinations of rational Dedekind-zeta invariants of hyperbolic manifolds and Feynman knots and links]<br>
 ** J.M. Borwein, D.J. Broadhurst, 1998
+* [http://www.springerlink.com/content/v36272439g3g5006/ Hyperbolic manifolds and special values of Dedekind zeta-functions]<br>
+** Don Zagier, Inventiones Mathematicae, Volume 83, Number 2 / 1986년 6월
+*  Commensurability classes and volumes of hyperbolic 3-manifolds<br>
+** A. Borel, Ann. Sc. Norm. Super. Pisa8, 1–33 (1981)
 * [[2010년 books and articles|논문정리]]