English

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!

R2 v1 2026-06-25T01:23:25.899Z