restriction to ${{\mathrm{SL}}}_3({\mathbb{A}})$ is a reflection of the fact that the the adjoint representation of ${{\mathrm{GL}}}_3({{\mathbb {C}}})$ factors through ${{\mathrm {P}}}{{\mathrm{GL}}}_3({{\mathbb {C}}})$, the $L$-group of ${{\mathrm{SL}}}_3$. Similarly, the local zeta integral $Z^*(W_v,f_{s,v})$ also only depends on $ W_v|_{{{\mathrm{SL}}}_3(F_v)}$.

To obtain the holomorphy of $L(s,\pi,{{\mathrm{Ad}}}\times \chi)$, on one hand, one needs to analyze the properties of the global integral $Z(\varphi,f_s)$; on the other hand, one needs to analyze the local zeta integral $Z^*(W_v,f_{s,v})$ at every ramified place $v$. Because of the functional equation, it suffices to rule out poles in the half plane ${{\mathrm{Re}}}(s) \ge \frac 12.$ After the pioneering work of Ginzburg [@G] and Ginzburg-Jiang [@GJ], some progress in this direction was obtained in [@H18]. The goal of our first main result in this paper is to extend [@H18 Theorem 6.1], which treats the partial $L$-function $L^S(s,\pi,{{\mathrm{Ad}}}\times \chi)=\prod_{v\notin S}L(s,\pi_v,{{\mathrm{Ad}}}\times \chi_v)$ attached to a finite set $S=S(\pi,\chi)$ of places of $F$. Here $S(\pi,\chi)$ contains the set of all infinite places $S_\infty$ and all of the ramified places of $\pi$ and $\chi$. The main result in [@H18] states that for $\chi =1$ or $\chi$ unitary and $\pi \not \cong \pi \times \chi,$ the function $L^S(s,\pi,{{\mathrm{Ad}}}\times \chi)$ has no poles on the region 