Ginzburg's conjecture on the unramified computation of Eulerian integrals

Colin Jia Sheng Loh

Ginzburg's conjecture on the unramified computation of Eulerian integrals

Number Theory 2026-07-30 v1

Authors: Colin Jia Sheng Loh

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.

Keywords

Ginzburg conjecture Eulerian integral unramified computation automorphic representation Speh representation

Cite

@article{arxiv.2607.28403,
  title  = {Ginzburg's conjecture on the unramified computation of Eulerian integrals},
  author = {Colin Jia Sheng Loh},
  journal= {arXiv preprint arXiv:2607.28403},
  year   = {2026}
}