On the sum of matrices of special linear group over finite field

被引：0

作者：

Luo, Yifan ^{[1
]}

Ji, Qingzhong ^{[1
]}

机构：

[1] Nanjing Univ, Dept Math, Nanjing 210000, Jiangsu, Peoples R China

来源：

AIMS MATHEMATICS | 2025年 / 10卷 / 02期

关键词：

ring of matrices; finite field; sum of matrices; Fourier transformation; Kloosterman sum; EXCEPTIONAL UNITS; GENERATORS; SUMSETS;

D O I：

10.3934/math.2025168

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let Fq be a finite field of q elements. For n E N* with n >= 2, let Mn := Matn(Fq) be the ring of matrices of order n over Fq, Gn,1 := S ln(Fq) be the special linear group over Fq. In this paper, by using the technique of Fourier transformation, we obtain a formula for the number of representations of any element of Mn as the sum of k matrices in Gn,1. As a corollary, we give another proof of the number of the third power moment of the classic Kloosterman sum.

引用

页码：3642 / 3651

页数：10

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