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

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