Bessel functions and Kloosterman integrals on GL(n)

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 [5] [6] [7], the theory of the (relative) Shalika germs established by H. Jacquet and Y. Ye in [25] [26] and G. Stevens' approach [35] on estimating certain GL(n) generalized Kloosterman sums. (c) 2023 The Author. Published by Elsevier Inc. This is an open access article under the CC BY license (http:// creativecommons .org /licenses /by /4 .0/).