Normal zeta functions of the Heisenberg groups over number rings I: the unramified case

  title={Normal zeta functions of the Heisenberg groups over number rings I: the unramified case},
  author={Michael M. Schein and Christopher Voll},
  journal={J. London Math. Society},
Let K be a number field with ring of integers OK . We compute the local factors of the normal zeta functions of the Heisenberg groups H(OK) at rational primes which are unramified in K. These factors are expressed as sums, indexed by Dyck words, of functions defined in terms of combinatorial objects such as weak orderings. We show that these local zeta functions satisfy functional equations upon the inversion of the prime. 

From This Paper

Topics from this paper.


Publications referenced by this paper.
Showing 1-10 of 13 references

Computing normal zeta functions of certain groups

  • T. Bauer
  • M.Sc. thesis, Bar-Ilan University
  • 2013
Highly Influential
4 Excerpts

Counting irreducible representations of the Heisenberg group over the integers of a quadratic number field

  • S. Ezzat
  • J. Algebra 397
  • 2014
Highly Influential
3 Excerpts

Combinatorics of Coxeter groups

  • A. Björner, F. Brenti
  • Graduate Texts in Mathematics, vol. 231, Springer…
  • 2005
Highly Influential
3 Excerpts

Subgroups of finite index in nilpotent groups

  • F. J. Grunewald, D. Segal, G. C. Smith
  • Invent. Math. 93
  • 1988
Highly Influential
3 Excerpts

Zeta functions of algebras and resolution of singularities

  • G. Taylor
  • Ph.D. thesis, University of Cambridge
  • 2001
1 Excerpt

Similar Papers

Loading similar papers…