Macedo Lins de Araujo, Paula
(2020)
Bivariate representation and conjugacy class zeta functions associated to unipotent group schemes, II: groups of type F, G, and H.
International Journal of Algebra and Computation, 30
(5).
pp. 931975.
ISSN 17936500
Full content URL: https://doi.org/10.1142/S0218196720500265
Bivariate representation and conjugacy class zeta functions associated to unipotent group schemes, II: groups of type F, G, and H  Authors' Accepted Manuscript   [Download] 

Preview 

PDF
bivariatezfII.pdf
 Whole Document
622kB 
Item Type:  Article 

Item Status:  Live Archive 

Abstract
This is the second of two papers introducing and investigating two bivariate zeta functions associated to unipotent group schemes over rings of integers of number fields. In the first part, we proved some of their properties such as rationality and functional equations. Here, we calculate such bivariate zeta functions of three infinite families of nilpotent groups of class 2 generalizing the Heisenberg group of (3×3)unitriangular matrices over rings of integers of number fields. The local factors of these zeta functions are also expressed in terms of sums over finite hyperoctahedral groups, which provide formulae for joint distributions of three statistics on such groups.
Repository Staff Only: item control page