PreprintCC BY 4.0arXiv
Bessel Distributions and Kloosterman Sums
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.
Related
- Kloosterman Sums and Plücker Height Zeta Functions
- Galois representations and modularity for twisted moments of Kloosterman sums
- Sums of Kloosterman sums formed with modular symbols
- Stevens' Approach to Kloosterman Sums on Split Groups
- Selberg sieve weights and sign changes of Kloosterman sums. II. Square-free moduli with at most four prime factors
BibTeX
@misc{cai2026bessel,
title = {{Bessel Distributions and Kloosterman Sums}},
author = {Li Cai and Jingsong Chai and Yadi Liu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.29852},
eprint = {2606.29852},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.29852},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Bessel Distributions and Kloosterman Sums
AU - Li Cai
AU - Jingsong Chai
AU - Yadi Liu
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2606.29852
UR - https://arxiv.org/abs/2606.29852
AB - 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.
ER -