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

Anne-Maria Ernvall-Hytönen, Jesse Jääsaari, Esa V. Vesalainen

Published 2014-05-28, updated 2014-08-06Version 2

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 $\Omega$-result for short sums of Fourier coefficients.