Zeta functions of groups and enumeration in Bruhat-Tits buildings

Details Zeta functions of groups and enumeration in Bruhat-Tits buildings Zeta functions of groups and enumeration in Bruhat-Tits buildings

2003-05-26

arxiv.org/abs/math/0305360v1

Mathematics

Group Theory

32 pages, 1 figure. To appear in Amer. J. Math

Scientific paper

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 Sl_n(Q_p). 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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