Proof of the Borwein-Broadhurst conjecture for a dilogarithmic integral arising in quantum field theory

Details Proof of the Borwein-Broadhurst conjecture for a dilogarithmic integral arising in quantum field theory Proof of the Borwein-Broadhurst conjecture for a dilogarithmic integral arising in quantum field theory

2010-10-31

arxiv.org/abs/1011.0195v1

Physics

Mathematical Physics

8 pages, 1 figure

Scientific paper

Borwein and Broadhurst, using experimental-mathematics techniques, in 1998 identified numerous hyperbolic 3-manifolds whose volumes are rationally related to values of various Dirichlet L series $\textup{L}_{d}(s)$. In particular, in the simplest case of an ideal tetrahedron in hyperbolic space, they conjectured that a dilogarithmic integral representing the volume equals to $\textup{L}_{-7}(2)$. Here we have provided a formal proof of this conjecture which has been recently numerically verified (to at least 19,995 digits, using 45 minutes on 1024 processors) in cutting-edge computing experiments. The proof essentially relies on the results of Zagier on the formula for the value of Dedekind zeta function $\zeta_{\mathbb{K}}(2)$ for an arbitrary field $\mathbb{K}$.

Affiliated with

Also associated with

No associations

Rating

Proof of the Borwein-Broadhurst conjecture for a dilogarithmic integral arising in quantum field theory does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Proof of the Borwein-Broadhurst conjecture for a dilogarithmic integral arising in quantum field theory, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Proof of the Borwein-Broadhurst conjecture for a dilogarithmic integral arising in quantum field theory will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-663973