Abstract: To every finitely generated group $G$ one can associate a zeta function counting subgroups of finite index in $G$. If $G$ is nilpotent, this zeta function decomposes as an Euler product into local factors. It is an open conjecture that for every class two nilpotent group almost all local factors of the associated zeta function satisfy a functional equation. The higher Heisenberg groups provide an instructive test case for the validity of this conjecture. I will report on joint work with Christopher Voll in this context, illustrating a geometric-combinatorial approach involving Bruhat-Tits buildings for symplectic groups over $p$-adic number fields. The talk will be aimed at a general audience. In particular, I will introduce and motivate the various mathematical structures mentioned in this abstract.