needs to analyze Ginzburg’s local zeta integral $Z(W_v,f_{s,v})$ for any archimedean place $v$. In this direction, recently F. Tian is able to show the meromorphic continuation, local functional equation at archimedean places in [@Ti18]. Moreover, the local gamma factors for principal series representations at archimedean places is explicitly computed in [@Tianthesis; @Ti18c]. ]{}

The second part of this paper is devoted to the nonsplit case, i.e., when $H={{\mathrm{SU}}}_{2,1}$ is a quasisplit unitary group attached to a quadratic extension $E$ of $F$, and $\pi$ is a globally generic, irreducible cuspidal automorphic representation of ${{\mathrm {U}}}_{2,1}({{\mathbb {A}}}).$ In this case, we have not performed a careful analysis on local zeta integrals at ramified primes, because there is still a lot to say about the simpler question of when the partial $L$ function attached to all finite unramified places will have a pole. As mentioned, the adaptation of Ginzburg’s integral representation to apply in nonsplit case was carried out in [@H12]. The adaptation of Ginzburg-Jiang’s method of ruling out poles was carried out in [@H18], with interesting results.

The key to Ginzburg and Jiang’s result is a “first term identity” relating residues of Eisenstein series attached to different parabolics. Using such an identity, 