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- Title
IDEAL ZETA FUNCTIONS ASSOCIATED TO A FAMILY OF CLASS-2-NILPOTENT LIE RINGS.
- Authors
Voll, Christopher
- 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.
- Subjects
NILPOTENT Lie groups; NILPOTENT groups; FUNCTIONAL equations; ZETA functions; TOPOLOGICAL entropy
- Publication
Quarterly Journal of Mathematics, 2020, Vol 71, Issue 3, p959
- ISSN
0033-5606
- Publication type
Article
- DOI
10.1093/qmathj/haaa010