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PreprintCC BY 4.0arXiv

Stevens' Approach to Kloosterman Sums on Split Groups

  • Li Cai
  • Haoran Liu
  • Mingyu Yang
  • Wenyan Yang
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Abstract

We develop a uniform framework for Stevens' approach to Kloosterman sums on split groups over p-adic fields. The main result reduces the bounding of Kloosterman sums to that for the so-called Plücker-constrained sets, which are certain subsets of affine spaces constrained by conditions giving by the Plücker coordinates. We then give a nontrivial bound for the Kloosterman sums on the exceptional group G2. As an application, we obtain the regularity of Bessel distributions associated with generic representations on G2.

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Cite

BibTeXRIS
BibTeX
@misc{cai2026stevens,
  title = {{Stevens' Approach to Kloosterman Sums on Split Groups}},
  author = {Li Cai and Haoran Liu and Mingyu Yang and Wenyan Yang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.24399},
  eprint = {2610.24399},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.24399},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Stevens' Approach to Kloosterman Sums on Split Groups
AU  - Li Cai
AU  - Haoran Liu
AU  - Mingyu Yang
AU  - Wenyan Yang
PY  - 2026
DA  - 2026/10/23
PB  - arXiv
DO  - 10.48550/arxiv.2610.24399
UR  - https://arxiv.org/abs/2610.24399
AB  - We develop a uniform framework for Stevens' approach to Kloosterman sums on split groups over p-adic fields. The main result reduces the bounding of Kloosterman sums to that for the so-called Plücker-constrained sets, which are certain subsets of affine spaces constrained by conditions giving by the Plücker coordinates. We then give a nontrivial bound for the Kloosterman sums on the exceptional group G_2. As an application, we obtain the regularity of Bessel distributions associated with generic representations on G_2.
ER  -