Ginzburg's conjecture on the unramified computation of Eulerian integrals

Abstract

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 ${\mathrm{GL}}_{2r}$ and the generalised Speh representation $\Delta ({\tau }_2,r)$ attached to a cuspidal automorphic representation ${\tau }_2$ of ${\mathrm{GL}}_2$. We also study an analogous Eulerian global integral involving degenerate Eisenstein series and compute its unramified local factors.