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Preprint Number 45

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45. Ehud Hrushovski and Ben Martin
Zeta functions from definable equivalence relations

Submission date: 3 January 2007


We prove that the theory of the p-adics Q_p, together with a set of explicitly given sorts, admits elimination of imaginaries. Using p-adic integration, we deduce the rationality of certain formal zeta functions arising from definable equivalence relations. As an application, we prove rationality results for zeta functions obtained by counting isomorphism classes of irreducible representations of finitely generated nilpotent groups; these are analogous to similar results of Grunewald, Segal and Smith for subgroup growth zeta functions of finitely generated nilpotent groups. (Preliminary version.)

Mathematics Subject Classification: 03C10; 20C15

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