  Let F be a local non-archimedean field. We prove a formula relating orbital
integrals in GL(n,F) (for the unit Hecke function) and the generating series
counting ideals of a certain ring. Using this formula, we give an explicit
estimate for such orbital integrals. We also derive an analogous formula for
global fields, proving analytic properties of the Dedekind zeta function for
orders in global fields.
