Poles of Eisenstein series on general linear groups induced from two Speh representations

We determine the poles of the Eisenstein series on a general linear group, induced from two Speh representations, $\mathrm{\Delta }(\tau ,m_1)\mathrm{\mid }\cdot {\mathrm{\mid }}^s\times \mathrm{\Delta }(\tau ,m_2)\mathrm{\mid }\cdot {\mathrm{\mid }}^{-s}$, $Re(s)\ge 0$, where $\tau$ is an irreducible, unitary, cuspidal, automorphic representation of $G{L}_n(\mathbf{A})$. The poles are simple and occur at $s=\frac{m_1+m_2}{4}-\frac{i}{2}$, $0\le i\le min(m_1,m_2)-1$. Our methods also show that when $m_1=m_2$, the above Eisenstein series vanish at s=0.