1301.5105 (Shu Oi et al.)

The hexagon equations for dilogarithms and the Riemann-Hilbert problem    [PDF]

Shu Oi, Kimio Ueno

In this article we present the hexagon equations for dilogarithms which come from the analytic continuation of the dilogarithm $\mathrm{Li}_2(z)$ to ${\mathbf P}^1 \setminus {0,1,\infty}$. The hexagon equations are shown to be equivalent to the coboundary relations for a 1-cocycle of holomorphic functions on ${\mathbf P}^1$. Hence to solve the hexagon equations is nothing but to solve a Riemann-Hilbert problem, and they uniquely characterize the dilogarithm.

View original: http://arxiv.org/abs/1301.5105