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.