Resonances and $\mathrm{\Omega }$-results for Exponential Sums Related to Maass Forms for $\mathrm{S}\mathrm{L}(n,\mathbb{Z})$

We obtain resonances for short exponential sums involving Fourier coefficients of Maass forms for $\mathrm{S}\mathrm{L}(n,\mathbb{Z})$. This involves deriving asymptotics for the integrals appearing in the $\mathrm{G}\mathrm{L}(n)$ Voronoi summation formula. As an application, we also prove an $\mathrm{\Omega }$-result for short sums of Fourier coefficients.