Gauss Sums on $GL_2(\mathbb{Z}/p^l\mathbb{Z})$

Taiki Maeda

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arXiv · 1303.5188

Gauss Sums on $GL_2(\mathbb{Z}/p^l\mathbb{Z})$

Taiki Maeda

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Abstract

We determine explicitly the Gauss sums on the general linear group $GL_2(\mathbb{Z}/p^l\mathbb{Z})$ 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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BibTeX RIS

Taiki Maeda. 2013-03-21. Gauss Sums on $GL_2(\mathbb{Z}/p^l\mathbb{Z})$. https://arxiv.org/abs/1303.5188

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