Gauss Sums on GL₂(ℤ/p^lℤ)

2013/03/21 by Taiki Maeda, Maeda, Taiki
Mathematics · #Advanced Algebra and Geometry #Finite Group Theory Research #Algebraic Geometry and Number Theory

paper · pdf · doi:10.48550/arxiv.1303.5188

Abstract

We determine explicitly the Gauss sums on the general linear group GL₂(ℤ/p^lℤ) for all irreducible characters, where p is an odd prime and l is an integer > 1. While there are several studies of the Gauss sums on finite algebraic groups defined over a finite field, this paper seems to be the first one which determines the Gauss sums on a matrix group over a finite ring.

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