• Corpus ID: 117524622

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

@article{Cvijovic2010ProofOT,
  title={Proof of the Borwein-Broadhurst conjecture for a dilogarithmic integral arising in quantum field theory},
  author={Djurdje Cvijovic},
  journal={arXiv: Mathematical Physics},
  year={2010}
}

• D. Cvijovic
• Published 31 October 2010
• Mathematics
• arXiv: Mathematical Physics

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 $\mathbb{K}$.