Bounds for Kloosterman sums on GL(n)
Number Theory
2023-11-27 v2
Abstract
This paper establishes power-saving bounds for Kloosterman sums associated with the long Weyl element for GL(n), as well as for another type of Weyl element of order 2. These bounds are obtained by establishing an explicit representation as exponential sums. As an application we go beyond Sarnak's density conjecture for the principal congruence subgroup of prime level. We also bound all Kloosterman sums for GL(4).
Cite
@article{arxiv.2208.01295,
title = {Bounds for Kloosterman sums on GL(n)},
author = {V. Blomer and S. H. Man},
journal= {arXiv preprint arXiv:2208.01295},
year = {2023}
}
Comments
some updates; to appear in Math. Ann