Gauss sums over some matrix groups
Number Theory
2011-05-24 v1 Combinatorics
Abstract
In this note, we give explicit expressions of Gauss sums for general (resp. special) linear groups over finite fields, which involves Gauss sums (resp. Kloosterman sums). The key ingredient is averaging such sums over Borel subgroups. As applications, we count the number of invertible matrices of zero-trace over finite fields and we also improve two bounds by Ferguson, Hoffman, Luca, Ostafe and Shparlinski in [ Some additive combinatorics problems in matrix rings, Rev. Mat. Complut. (23) 2010, 501--513 ].
Cite
@article{arxiv.1105.4513,
title = {Gauss sums over some matrix groups},
author = {Yan Li and Su Hu},
journal= {arXiv preprint arXiv:1105.4513},
year = {2011}
}
Comments
9 pages