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. [ABSTRACT FROM AUTHOR]