Resonance and rapid decay of exponential sums of Fourier coefficients of a Maass form for $G{L}_m(\mathbb{Z})$

Xiumin Ren, Yangbo Ye

Let $f$ be a full-level cusp form for $G{L}_m(\mathbb{Z})$ with Fourier coefficients $A_f(n_1,...,n_{m-1})$. In this paper an asymptotic expansion of Voronoi's summation formula for $…