Year: 2026
Type: preprint
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 $G_2$. As an application, we obtain the regularity of Bessel distributions associated with generic representations on $G_2$.
Source: arXiv (Cornell University)
Authors: Cai, Li, Liu, Haoran, Yang, Mingyu, Yang, Wenyan
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Peking University
OpenAlex ID: W7222995705