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	Gauss sum of index 4: (2) non-cyclic case
	Yang, J ; Luo, SX ; Feng, KQ
	2010-05-06 ; 2010-05-06
关键词	Gauss sum Stickelberger Theorem Davenport-Hasse formula class number of imaginary quadratic field Mathematics, Applied Mathematics
中文摘要	Assume that, m >= 2, p is a prime number, (m, p(p - 1)) = 1, -1 is not an element of < p > subset of (Z/mZ)* and [(Z/mZ)* : < p >] = 4. In this paper, we calculate the value of Gauss sum G(x) = Sigma(x is an element of F;) X(x)zeta(T(x))(P) over F-q, where q = p(f), f = rho(m)/4, X is a multiplicative character of Fq and T is the trace map from F-q to F-p. Under our assumptions, G(X) belongs to the decomposition field K of p in and K is an imaginary quartic abelian number field. When the Galois group Gal(K/Q) is cyclic, we have studied this cyclic case in another 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.
语种	英语 ; 英语
出版者	SPRINGER HEIDELBERG ; HEIDELBERG ; TIERGARTENSTRASSE 17, D-69121 HEIDELBERG, GERMANY
内容类型	期刊论文
源URL	[http://hdl.handle.net/123456789/13871]
专题	清华大学
推荐引用方式 GB/T 7714	Yang, J,Luo, SX,Feng, KQ. Gauss sum of index 4: (2) non-cyclic case[J],2010, 2010.
APA	Yang, J,Luo, SX,&Feng, KQ.(2010).Gauss sum of index 4: (2) non-cyclic case..
MLA	Yang, J,et al."Gauss sum of index 4: (2) non-cyclic case".(2010).

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