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Zeta functions of groups and enumeration in Bruhat-Tits buildings

Zeta functions of groups and enumeration in Bruhat-Tits buildings
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. 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.
zeta functions of groups, bruhat-tits buildings
0002-9327
1005-1032
Voll, Christopher
b7bd2890-38ac-4e05-adb7-3b376916ff79
Voll, Christopher
b7bd2890-38ac-4e05-adb7-3b376916ff79

Voll, Christopher (2004) Zeta functions of groups and enumeration in Bruhat-Tits buildings. American Journal of Mathematics, 126 (5), 1005-1032. (doi:10.1353/ajm.2004.0041).

Record type: Article

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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Published date: October 2004
Keywords: zeta functions of groups, bruhat-tits buildings

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Local EPrints ID: 42193
URI: http://eprints.soton.ac.uk/id/eprint/42193
ISSN: 0002-9327
PURE UUID: dc0a762a-754e-4fee-a42c-02fd3a66fd5e

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Date deposited: 23 Nov 2006
Last modified: 15 Mar 2024 08:46

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Author: Christopher Voll

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