Pro-isomorphic zeta functions of some D^\ast Lie lattices of even rank.

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) \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. [ABSTRACT FROM AUTHOR]