Bessel Distributions and Kloosterman Sums

Li Cai; Jingsong Chai; Yadi Liu

Bessel Distributions and Kloosterman Sums

Number Theory 2026-06-29 v1 Representation Theory

Authors: Li Cai , Jingsong Chai , Yadi Liu

Abstract

Let $G$ be a split reductive group over a $p$ -adic field. We give germ expansions of Kloosterman integrals for $G$ . As an application, we prove that Bessel distributions are regular for all generic representations on $G$ provided that Kloosterman sums for any Levi subgroups of $G$ have nontrivial bounds.

Cite

@article{arxiv.2606.29852,
  title  = {Bessel Distributions and Kloosterman Sums},
  author = {Li Cai and Jingsong Chai and Yadi Liu},
  journal= {arXiv preprint arXiv:2606.29852},
  year   = {2026}
}

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36 pages