Bounds for Kloosterman Sums for ${\mathrm{G}\mathrm{L}}_n$

In this paper power saving bounds for general Kloosterman sums for all Weyl elements for ${\mathrm{G}\mathrm{L}}_n$ for $n>2$ are proven, improving the trivial bound by Dąbrowski and Reeder. This is achieved by representing the sums in an explicit way as exponential sums and bounding these through applications of the Weil bound.