An asymptotic orthogonality relation for Fourier coefficients of GL(n) Maas forms

In joint work with Dorian Goldfeld, we use the Kuznetsov trace formula
for GL(4) to prove an orthogonality relation on the Fourier coefficients
of GL(4) Maass forms.  This work has applications to low lying zeros and
symmetry types of L-functions, the equidistribution of Fourier
coefficients (vertical Sato-Tate) and more.  I will give some historical
background for the cases n=2,3, discuss the general setup for GL(n), and
explain our strategy generally and how it is carried out in the case of n=4.