Bessel Functions and Kloosterman Integrals on GL(n)
Number Theory
2023-11-29 v4 Representation Theory
Abstract
This paper will focus on the proof of local integrability of Bessel functions for GL(n) (p-adic case) by using the relations between Bessel functions and local Kloosterman (orbital) integrals proved in several papers of E. M. Baruch [Ba03] [Ba04] [Ba05], the theory of the (relative) Shalika germs established by H. Jacquet and Y. Ye in [JY96] [JY99] and G. Stevens' approach [Ste87] on estimating certain GL(n) generalized Kloosterman sums.
Cite
@article{arxiv.2208.01016,
title = {Bessel Functions and Kloosterman Integrals on GL(n)},
author = {Xinchen Miao},
journal= {arXiv preprint arXiv:2208.01016},
year = {2023}
}
Comments
46 pages. Accepted version. To appear in Journal of Functional Analysis. Comments are very welcome!