文献类型：期刊文献

英文题名：Complete solving of explicit evaluation of Gauss sums in the index 2 case

作者：Yang Jing[2,3];Xia LingLi[1]

第一作者：Yang Jing

通讯作者：Xia, LL[1]

机构：[1]Beijing Union Univ, Basic Courses Dept, Beijing 100101, Peoples R China;[2]Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China;[3]Nanyang Technol Univ, Sch Phys & Math Sci, Div Math Sci, Singapore 637371, Singapore

第一机构：北京联合大学基础教学部

通讯机构：[1]corresponding author), Beijing Union Univ, Basic Courses Dept, Beijing 100101, Peoples R China.|[1141788]北京联合大学基础教学部;[11417]北京联合大学;

年份：2010

卷号：53

期号：9

起止页码：2525-2542

外文期刊名：SCIENCE CHINA-MATHEMATICS

收录：;Scopus(收录号：2-s2.0-80053994322);WOS:【SCI-EXPANDED(收录号:WOS:000281670200027)】；

基金：This work was supported by National Natural Science Foundation of China (Grant No. 10990011) and the PhD Programs Foundation of Ministry of Education of China (Grant No. 20090002120013).

语种：英文

外文关键词：Gauss sum; Stickelberger's theorem; Stickelberger congruence; Davenport-Hasse lifting formula; Davenport-Hasse product formula

摘要：Let p be a prime number, N be a positive integer such that gcd( N, p) = 1, q = p(f) where f is the multiplicative order of p modulo N. Let. be a primitive multiplicative character of order N over finite field F(q). This paper studies the problem of explicit evaluation of Gauss sums G(chi) in the "index 2 case" (i.e. [(Z/NZ)* : < p >] = 2). Firstly, the classification of the Gauss sums in the index 2 case is presented. Then, the explicit evaluation of Gauss sums G(chi(lambda)) ( 1 <= lambda <= N - 1) in the index 2 case with order N being general even integer (i.e. N = 2(r) . N(0), where r, N(0) are positive integers and N(0) >= 3 is odd) is obtained. Thus, combining with the researches before, the problem of explicit evaluation of Gauss sums in the index 2 case is completely solved.