  We describe an approach to express the geometric side of the Arthur-Selberg
trace formula in terms of zeta integrals attached to prehomogeneous vector
spaces. This will provide explicit formulas for weighted orbital integrals and
for the coefficients by which they are multiplied in the trace formula. We
implement this programme for the principal unipotent conjugacy class. The
method relies on certain convergence results and uses the notions of induced
conjugacy classes and canonical parabolic subgroups. So far, it works for
certain types of conjugacy classes, which covers all classes appearing in
classical groups of absolute rank up to two.
