Generating Functions on Covering Groups

In this paper we prove Conjecture 1.2 in \cite{B-F}. This enables us to establish the meromorphic continuation of the standard partial $L$ function $L^S(s,{\pi }^{(n)})$. Here, ${\pi }^{(n)}$ is a genuine irreducible cuspidal representation of the group $G{L}_r^{(n)}(\mathbf{A})$.