| Gauss Sum of Index 4： （2） Non-cyclic Case |
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| 作者姓名： | Jing YANG Shi Xin LUO Ke Qin FENG |
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| 作者单位： | Department of Mathematical Science, Tsinghua University, Beijing 100084, P. R. China |
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| 基金项目： | This work is supported by the National Fundamental Scientific Research Project of China （2004CB318000） and the NSFC Grant 60276016 |
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| 摘 要： | Assume that m ≥ 2, p is a prime number, （m,p（p - 1）） = 1,-1 not belong to 〈p〉 belong to （Z/mZ）^＊ and （Z/mZ）^＊：〈p〉]=4.In this paper, we calculate the value of Gauss sum G（X）=∑x∈F^＊x（x）ζp^T（x） over Fq,where q=p^f,f=φ（m）/4,x is a multiplicative character of Fq and T is the trace map from Fq to Fp.Under our assumptions,G（x） belongs to the decomposition field K of p in Q（ζm） and K is an imaginary quartic abelian unmber field.When the Galois group Gal（K/Q） is cyclic,we have studied this cyclic case in anotyer paper：＂Gauss sums of index four：（1）cyclic case＂（accepted by Acta Mathematica Sinica,2003）.In this paper we deal with the non-cyclic case.
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| 关 键 词： | 高斯求和 Davenport-Hawse公式 假象二次方程式场 素数 代数学 Stickelberger定理 |
| 收稿时间： | 2004-01-09 |
| 修稿时间： | 2004-01-092005-03-22 |
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