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

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

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 a…