Local Jacquet-Shalika integrals and modifying factors

Abstract

Over any local field of characteristic zero, we develop a local theory of Jacquet-Shalika integrals that were originally introduced by Jacquet and Shalika to study exterior square local $L$-factors for $G{L}_m$. In particular, at least in the archimedean case, we establish a complete functional equation matching Artin local $\epsilon$-factors. Central to the argument is a novel comparison strategy between Jacquet-Shalika integrals and open-orbit integrals associated to the Shalika subgroup.

arXiv commentThis paper is essentially part of arXiv:2509.00434 with revisions; we now decide to make it an independent paper