Zeta functions of groups and enumeration in Bruhat-Tits buildings
Christopher Voll
Abstract
We introduce a new method to calculate local normal zeta functions of finitely generated, torsion-free nilpotent groups. It is based on an enumeration of vertices in the Bruhat-Tits building for Sln(Qp). It enables us to give explicit computations for groups of class 2 with small centres and to derive local functional equations. Examples include formulae for non-uniform normal zeta functions.
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