摘要
Let p be a prime number,N be a positive integer such that gcd(N,p) = 1,q = pf where f is the multiplicative order of p modulo N.Let χ be a primitive multiplicative character of order N over finite field Fq.This paper studies the problem of explicit evaluation of Gauss sums G(χ) 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(χλ)(1 λ N-1) in the index 2 case with order N being general even integer(i.e.N = 2r·N0,where r,N0 are positive integers and N0 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.
Let p be a prime number,N be a positive integer such that gcd(N,p) = 1,q = pf where f is the multiplicative order of p modulo N.Let χ be a primitive multiplicative character of order N over finite field Fq.This paper studies the problem of explicit evaluation of Gauss sums G(χ) in the "index 2 case"(i.e.[(Z/NZ):] = 2).Firstly,the classification of the Gauss sums in the index 2 case is presented.Then,the explicit evaluation of Gauss sums G(χλ)(1 λ N-1) in the index 2 case with order N being general even integer(i.e.N = 2r·N0,where r,N0 are positive integers and N0 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.
作者
YANG Jing1,2 & XIA LingLi3,1Department of Mathematical Sciences,Tsinghua University,Beijing 100084,China
2Division of Mathematical Sciences,School of Physical and Mathematical Sciences,Nanyang Technological University,637371,Singapore
3Basic Courses Department,Beijing Union University,Beijing 100101,China
基金
supported by National Natural Science Foundation of China (Grant No.10990011)
the PhD Programs Foundation of Ministry of Education of China (Grant No. 20090002120013)
