Witten's formula, cohomological pairings for flat connections and applications of multiple zeta functions

We use Witten's volume formula to calculate the cohomological pairings of the moduli space of flat $SU(3)$ connections. The cohomological pairings of moduli space of flat $SU(2)$ connections is known from the work of Thaddeus-Witten-Donaldson, but for higher holonomy groups these pairings are largely unknown. We make some progress on these problems, and show that the pairings can be expressed in terms of multiple zeta functions.