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.

arXiv comment45 pages, V2: The results have been significantly improved and several key notions have been made clearer. We now can prove the regularity of the Bessel distributions for split groups of type A