scholarly journals Pro-isomorphic zeta functions of nilpotent groups and Lie rings under base extension

2021 ◽  
pp. 1
Author(s):  
Mark N. Berman ◽  
Itay Glazer ◽  
Michael M. Schein
Keyword(s):  
Zeta Functions ◽  
Nilpotent Groups ◽  
Lie Rings ◽  
Base Extension

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.

On connection between nilpotent groups and Lie rings

2000 ◽  
Vol 41 (5) ◽  
pp. 994-1004 ◽  
Author(s):  
A. Jaikin Zapirain ◽  
E. I. Khukhro
Keyword(s):  
Nilpotent Groups ◽  
Lie Rings

scholarly journals Representation zeta functions of some nilpotent groups associated to prehomogeneous vector spaces

2017 ◽  
Vol 29 (3) ◽  
Author(s):  
Alexander Stasinski ◽  
Christopher Voll
Keyword(s):  
Zeta Functions ◽  
Nilpotent Groups ◽  
Number Fields ◽  
Vector Spaces ◽  
Unipotent Group ◽  
Finitely Generated ◽  
Group Schemes ◽  
Prehomogeneous Vector Spaces ◽  
Rings Of Integers

AbstractWe compute the representation zeta functions of some finitely generated nilpotent groups associated to unipotent group schemes over rings of integers in number fields. These group schemes are defined by Lie lattices whose presentations are modelled on certain prehomogeneous vector spaces. Our method is based on evaluating

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