Witten zeta function

For a finite group
Suppose $$G$$ is a finite group. The Witten zeta function of $$G$$, denoted $$\zeta_G$$, is the function:

$$s \mapsto \sum_{\rho \in \operatorname{Irr}(G)} \frac{1}{(\operatorname{deg}(\rho))^s}$$

In other words, it is a sum of the $$(-s)^{th}$$ powers of the degrees of irreducible representations of $$G$$.