Geodesic
Functional equations for zeta functions of groups and rings
Christopher Voll1
1 School of Mathematics<br/>University of Southampton<br/>Highfield, SO17 1BJ<br/>United Kingdom
Annals of mathematics, Tome 172 (2010) no. 2, pp. 1181-1218.

Voir la notice de l'article provenant de la source Annals of Mathematics website

We introduce a new method to compute explicit formulae for various zeta functions associated to groups and rings. The specific form of these formulae enables us to deduce local functional equations. More precisely, we prove local functional equations for the subring zeta functions associated to rings, the subgroup, conjugacy and representation zeta functions of finitely generated, torsion-free nilpotent (or $\mathcal{T}$-)groups, and the normal zeta functions of $\mathcal{T}$-groups of class $2$. We deduce our theorems from a “blueprint result” on certain $p$-adic integrals which generalises work of Denef and others on Igusa’s local zeta function. The Malcev correspondence and a Kirillov-type theory developed by Howe are used to “linearise” the problems of counting subgroups and representations in $\mathcal{T}$-groups, respectively.
DOI : 10.4007/annals.2010.172.1181

Christopher Voll 1

1 School of Mathematics<br/>University of Southampton<br/>Highfield, SO17 1BJ<br/>United Kingdom 
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Christopher Voll. Functional equations for zeta functions of groups and rings. Annals of mathematics, Tome 172 (2010) no. 2, pp. 1181-1218. doi : 10.4007/annals.2010.172.1181. http://geodesic.mathdoc.fr/articles/10.4007/annals.2010.172.1181/

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