Research Training Network in Model Theory
Publications > Preprint server > Preprint Number 45

Preprint Number 45

Previous Next Preprint server

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

Keywords and phrases:

Full text: arXiv.

Last updated: March 23 2021 09:22 Please send your corrections to: