Macedo Lins de Araujo, Paula (2019) Bivariate representation and conjugacy class zeta functions associated to unipotent group schemes, I: arithmetic properties. Journal of Group Theory, 22 (4). pp. 741774. ISSN 14335883
Full content URL: https://doi.org/10.1515/jgth20180115
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Item Type:  Article 

Item Status:  Live Archive 
Abstract
This is the first of two papers in which we introduce and study two bivariate zeta functions associated to unipotent group schemes over rings of integers of number fields. One of these zeta functions encodes the numbers of isomorphism classes of irreducible complex representations of finite dimensions of congruence quotients of the associated group and the other one encodes the numbers of conjugacy classes of each size of such quotients. In this paper, we show that these zeta functions satisfy Euler factorizations and almost all of their Euler factors are rational and satisfy functional equations. Moreover, we show that such bivariate zeta functions specialize to (univariate) class number zeta functions. In case of nilpotency class 2, bivariate representation zeta functions also specialize to (univariate) twist representation zeta functions.
Keywords:  Finitely generated nilpotent groups, zeta functions, conjugacy classes, irreducible complex characters, Kirillov orbit method, padic integration 

Subjects:  G Mathematical and Computer Sciences > G110 Pure Mathematics 
Divisions:  College of Science > School of Mathematics and Physics 
ID Code:  47800 
Deposited On:  16 Feb 2022 15:45 
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