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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 GLm. In particular, at least in the archimedean case, we establish a complete functional equation matching Artin local ε-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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Cite

BibTeXRIS
BibTeX
@misc{jiang2026local,
  title = {{Local Jacquet-Shalika integrals and modifying factors}},
  author = {Dihua Jiang and Dongwen Liu and Binyong Sun and Fangyang Tian},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.05220},
  eprint = {2609.05220},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.05220},
}
RIS
TY  - UNPB
TI  - Local Jacquet-Shalika integrals and modifying factors
AU  - Dihua Jiang
AU  - Dongwen Liu
AU  - Binyong Sun
AU  - Fangyang Tian
PY  - 2026
DA  - 2026/09/04
PB  - arXiv
DO  - 10.48550/arxiv.2609.05220
UR  - https://arxiv.org/abs/2609.05220
AB  - 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 ε-factors. Central to the argument is a novel comparison strategy between Jacquet-Shalika integrals and open-orbit integrals associated to the Shalika subgroup.
ER  -