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.