Let $F$ be a number field. Let $\pi$ be a cuspidal automorphic representation of $GL_n(\mathbb{A_F})$. Do we know that $L(s,\pi\times \tilde\pi)$ has a simple pole at $s=1$? Do we know that $\frac{L(s,\pi\times \tilde\pi)}{\zeta_F(s)}$ is holomorphic at $s=1$?