Pro-isomorphic zeta functions of some 𝐷* Lie lattices of even rank

Abstract

We compute the local pro-isomorphic zeta functions at all but finitely many primes for a family of class-two-nilpotent Lie lattices of even rank, parametrized by irreducible monic non-linear polynomials f ( x ) ∈ Z [ x ] f(x) \in \mathbb {Z}[x] . These Lie lattices correspond to a family of groups introduced by Grunewald and Segal. The result is expressed in terms of a combinatorially defined family of rational functions.