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arXiv · 2609.05220

Local Jacquet-Shalika integrals and modifying factors

Dihua Jiang·Dongwen Liu·Binyong Sun·Fangyang Tian
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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 $GL_m$. In particular, at least in the archimedean case, we establish a complete functional equation matching Artin local $\varepsilon$-factors. Central to the argument is a novel comparison strategy between Jacquet-Shalika integrals and open-orbit integrals associated to the Shalika subgroup.

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Dihua Jiang, Dongwen Liu, Binyong Sun, Fangyang Tian. 2026-09-04. Local Jacquet-Shalika integrals and modifying factors. https://arxiv.org/abs/2609.05220

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