Zeta functions of groups and enumeration in Bruhat-Tits buildings

Christopher Voll

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arXiv · math/0305360

Zeta functions of groups and enumeration in Bruhat-Tits buildings

Christopher Voll

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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 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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Christopher Voll. 2003-05-26. Zeta functions of groups and enumeration in Bruhat-Tits buildings. https://arxiv.org/abs/math/0305360

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