Karl Dilcher, Dalhousie University

Derivatives and fast evaluation of the Witten zeta function
We study analytic properties of the Witten zeta function ${\mathcal W}(r,s,t)$, which is also named after Mordell and Tornheim. In particular, we evaluate the function ${\mathcal W}(s,s,\tau s)$ ($\tau>0$) at $s=0$ and, as our main result, find the derivative of this function at $s=0$, which turns out to be surprisingly simple. These results were first conjectured using high-precision calculations based on an identity due to Crandall that involves a free parameter and provides an analytic continuation. This identity was also the main tool in the eventual proofs of our results. Finally, we derive special values of a permutation sum and study an alternating analogue of ${\mathcal W}(r,s,t)$. (Joint work with Jon Borwein).