Zeta functions of groups - singular Pfaffians
Group Theory
2016-09-07 v1
Abstract
The local normal zeta functions of a finitely generated, torsion-free nilpotent group of class 2 depend on the geometry of the Pfaffian hypersurface associated to the bilinear form induced by taking commutators in . The smallest examples of zeta functions which are not finitely uniform arise from groups whose associated Pfaffian hypersurfaces are plane curves. In this paper we study groups whose Pfaffians define singular curves, illustrating that the local normal zeta functions may indeed invoke all the degeneracy loci of the Pfaffian.
Cite
@article{arxiv.math/0309471,
title = {Zeta functions of groups - singular Pfaffians},
author = {Christopher Voll},
journal= {arXiv preprint arXiv:math/0309471},
year = {2016}
}