  For $\alpha\geq 1$, let $g:\mathbb N\to\mathbb R_+$ be given by $g(0)=0$,
$g(1)=1$, $g(k)=(k/k-1)^\alpha$, $k\geq 2$. Consider the symmetric nearest
neighbour zero range process on the discrete torus $\mathbb T_L$ in which a
particle jumps from a site, occupied by $k$ particles, to one of its neighbors
with rate $g(k)$. Armend\'ariz and Loulakis\cite{al09} proved a strong form of
the equivalence of ensembles for the invariant measure of the supercritical
zero range process with $\alpha>2$. We generalize their result to all
$\alpha\geq 1$.
