Resonances and Ω-results for exponential sums related to Maass forms for SL(n,Z)

We obtain resonances for short exponential sums weighted by Fourier coefficients of Maass forms for SL(n,Z). This involves deriving asymptotics for the integrals appearing in the GL(n) Voronoi summation formula. As an application, we also prove an Ω-result for short sums of Fourier coefficients.