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

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

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