scholarly journals Functional equations for local normal zeta functions of nilpotent groups

2005 ◽  
Vol 15 (1) ◽  
pp. 274-295 ◽  
Author(s):  
C. Voll ◽  
A. Beauville
Keyword(s):  
Functional Equations ◽  
Zeta Functions ◽  
Nilpotent Groups

scholarly journals IDEAL ZETA FUNCTIONS ASSOCIATED TO A FAMILY OF CLASS-2-NILPOTENT LIE RINGS

2020 ◽  
Vol 71 (3) ◽  
pp. 959-980
Author(s):  
Christopher Voll
Keyword(s):  
Functional Equations ◽  
Zeta Functions ◽  
Infinite Family ◽  
Nilpotent Groups ◽  
Unipotent Group ◽  
Group Schemes ◽  
Lie Rings ◽  
Local Functional ◽  
Explicit Formulae ◽  
Local Functional Equations

Abstract We produce explicit formulae for various ideal zeta functions associated to the members of an infinite family of class-$2$-nilpotent Lie rings, introduced in M. N. Berman, B. Klopsch and U. Onn (A family of class-2 nilpotent groups, their automorphisms and pro-isomorphic zeta functions, Math. Z. 290 (2018), 909935), in terms of Igusa functions. As corollaries we obtain information about analytic properties of global ideal zeta functions, local functional equations, topological, reduced and graded ideal zeta functions, as well as representation zeta functions for the unipotent group schemes associated to the Lie rings in question.

scholarly journals Bivariate representation and conjugacy class zeta functions associated to unipotent group schemes, II: Groups of type F, G, and H

2020 ◽  
Vol 30 (05) ◽  
pp. 931-975
Author(s):  
Paula Macedo Lins de Araujo
Keyword(s):  
Conjugacy Class ◽  
Functional Equations ◽  
Zeta Functions ◽  
Nilpotent Groups ◽  
Number Fields ◽  
Unipotent Group ◽  
Group Schemes ◽  
Local Factors ◽  
Joint Distributions ◽  
Rings Of Integers

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 [Formula: see text] generalizing the Heisenberg group of ([Formula: see text])-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.

scholarly journals Functional equations of Weng's zeta functions for (G,P)/Q

2013 ◽  
Vol 135 (4) ◽  
pp. 1019-1038 ◽  
Author(s):  
Yasushi Komori
Keyword(s):  
Functional Equations ◽  
Zeta Functions
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