Jack Buttcane (Maine)

The Bessel functions are invariants of automorphic representations of a given group and appear in the Kuznetsov (relative trace) formulas associated with that group.  I will discuss the current status of their definition, construction, properties and applications on GL(n).  These are classical on GL(2), theorems on GL(3), in progress on GL(4) and conjectures on GL(n) and I will describe how I hope to extend the known results to the general case.