Voronoi formulas on GL(n)

We give a new, simple, purely analytic proof of the Voronoi formula for Maass forms on GL(3) first derived by Miller and Schmid. Our method is based on two lemmas of the first author and Thillainatesan which appear in their recent nonadelic proof of the converse theorem on GL(3). Using a different, even simpler method we derive Voronoi formulas on GL(n) twisted by additive characters of prime conductors. We expect that this method will work in general. In the final section of the paper Voronoi formulas on GL(n) are obtained, but in this case, the twists are by automorphic forms from lower rank groups.