  We introduce and study multivariate zeta functions enumerating
subrepresentations of integral quiver representations. For nilpotent such
representations defined over number fields, we exhibit a homogeneity condition
that we prove to be sufficient for local functional equations of the generic
Euler factors of these zeta functions. This generalizes and unifies previous
work on submodule zeta functions including, specifically, ideal zeta functions
of nilpotent (Lie) rings and their graded analogues.
