Zeta functions of groups and enumeration in Bruhat-Tits buildings

We introduce a new method to calculate local normal zeta functions of finitely generated, torsion-free nilpotent groups, [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /]-groups in short. It is based on an enumeration of vertices in the Bruhat-Tits building for [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="02i" /]. It enables us to give explicit computations for [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="03i" /]-groups of class 2 with small centres and to derive local functional equations. Examples include formulae for nonuniform normal zeta functions.