Bounds for Kloosterman Sums for $\mathrm{GL}_n$
Number Theory
2025-10-07 v2
Abstract
In this paper power saving bounds for general Kloosterman sums for all Weyl elements for for are proven, improving the trivial bound by D\k{a}browski 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.
Cite
@article{arxiv.2412.04976,
title = {Bounds for Kloosterman Sums for $\mathrm{GL}_n$},
author = {Johannes Linn},
journal= {arXiv preprint arXiv:2412.04976},
year = {2025}
}
Comments
V2: Added a uniform bound. Added a subsection on character dependency. Added further examples and explanations of the main ideas. Some minor changes