On the fourth-order linear recurrence formula related to classical Gauss sums

被引：47

作者：

Chen Zhuoyu ^{[1
]}

Zhang Wenpeng ^{[1
]}

机构：

[1] Northwest Univ Xian, Sch Math, Xian, Shaanxi, Peoples R China

来源：

OPEN MATHEMATICS | 2017年 / 15卷

关键词：

The classical Gauss sums; Fourth-order linear recurrence formula; Analytic method; Character sums;

D O I：

10.1515/math-2017-0104

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let p be an odd prime with p equivalent to 1 mod 4, k be any positive integer, psi be any fourth-order character mod p. In this paper, we use the analytic method and the properties of character sums mod p to study the computational problem of G (k, p) = tau(k) (psi) + tau(k) ((psi) over bar) and give an interesting fourth-order linear recurrence formula for it, where tau(psi) denotes the classical Gauss sums.

引用

页码：1251 / 1255

页数：5

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