Bivariate representation and conjugacy class zeta functions associated to unipotent group schemes, I: Arithmetic properties

Lins de Araujo PM (2019)
JOURNAL OF GROUP THEORY 22(4): 741-774.

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Zeitschriftenaufsatz | Veröffentlicht | Englisch
Abstract / Bemerkung
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.
Erscheinungsjahr
Zeitschriftentitel
JOURNAL OF GROUP THEORY
Band
22
Ausgabe
4
Seite(n)
741-774
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Lins de Araujo PM. Bivariate representation and conjugacy class zeta functions associated to unipotent group schemes, I: Arithmetic properties. JOURNAL OF GROUP THEORY. 2019;22(4):741-774.
Lins de Araujo, P. M. (2019). Bivariate representation and conjugacy class zeta functions associated to unipotent group schemes, I: Arithmetic properties. JOURNAL OF GROUP THEORY, 22(4), 741-774. doi:10.1515/jgth-2018-0115
Lins de Araujo, P. M. (2019). Bivariate representation and conjugacy class zeta functions associated to unipotent group schemes, I: Arithmetic properties. JOURNAL OF GROUP THEORY 22, 741-774.
Lins de Araujo, P.M., 2019. Bivariate representation and conjugacy class zeta functions associated to unipotent group schemes, I: Arithmetic properties. JOURNAL OF GROUP THEORY, 22(4), p 741-774.
P.M. Lins de Araujo, “Bivariate representation and conjugacy class zeta functions associated to unipotent group schemes, I: Arithmetic properties”, JOURNAL OF GROUP THEORY, vol. 22, 2019, pp. 741-774.
Lins de Araujo, P.M.: Bivariate representation and conjugacy class zeta functions associated to unipotent group schemes, I: Arithmetic properties. JOURNAL OF GROUP THEORY. 22, 741-774 (2019).
Lins de Araujo, Paula Macêdo. “Bivariate representation and conjugacy class zeta functions associated to unipotent group schemes, I: Arithmetic properties”. JOURNAL OF GROUP THEORY 22.4 (2019): 741-774.