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res:
bibo_abstract:
- We study representation zeta functions of finitely generated, torsion-free nilpotent
groups which are groups of rational points of unipotent group schemes over rings
of integers of number fields. Using the Kirillov orbit method and p-adic integration,
we prove rationality and functional equations for almost all local factors of
the Euler products of these zeta functions. We further give explicit formulae,
in terms of Dedekind zeta functions, for the zeta functions of class-2-nilpotent
groups obtained from three infinite families of group schemes, generalizing the
integral Heisenberg group. As an immediate corollary, we obtain precise asymptotics
for the representation growth of these groups, and key analytic properties of
their zeta functions, such as meromorphic continuation. We express the local factors
of these zeta functions in terms of generating functions for finite Weyl groups
of type B. This allows us to establish a formula for the joint distribution of
three functions, or "statistics", on such Weyl groups. Finally, we compare our
explicit formulae to p-adic integrals associated to relative invariants of three
infinite families of prehomogeneous vector spaces.@eng
bibo_authorlist:
- foaf_Person:
foaf_givenName: A.
foaf_name: Stasinski, A.
foaf_surname: Stasinski
- foaf_Person:
foaf_givenName: Christopher
foaf_name: Voll, Christopher
foaf_surname: Voll
foaf_workInfoHomepage: http://www.librecat.org/personId=27296433
bibo_doi: 10.1353/ajm.2014.0010
bibo_issue: '2'
bibo_volume: 136
dct_date: 2014^xs_gYear
dct_identifier:
- UT:000333657000007
dct_isPartOf:
- http://id.crossref.org/issn/0002-9327
dct_language: eng
dct_publisher: Muse - Johns Hopkins University Press@
dct_title: Representation zeta functions of nilpotent groups and generating functions
for Weyl groups of type B@
...