We prove Witten zeta function of a root system $\Phi$ has high-order vanishing at negative even integers, using an integral representation involving the Hurwitz zeta function. This settles a conjecture of Kurokawa and Ochiai for a large class of compact Lie groups. We also provide a qualitative description of the corresponding leading coefficient in terms of Riemann zeta values, in which the highest root of $\Phi$ makes a natural appearance.
Categories: math.NT math.CA