Ginzburg's conjecture on the unramified computation of Eulerian integrals

In this paper, we prove a conjecture of D. Ginzburg on the unramified computation of an Eulerian global integral associated with a cuspidal automorphic representation of ${\mathrm{G}\mathrm{L}}_{2r}$ and the generalised Speh representation $\mathrm{\Delta }({\tau }_2,r)$ attached to a cuspidal automorphic representation ${\tau }_2$ of ${\mathrm{G}\mathrm{L}}_2$. We also study an analogous Eulerian global integral involving degenerate Eisenstein series and compute its unramified local factors.