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	8-ranks of class groups of some imaginary quadratic number fields
	Xi Mei Wu; Qin Yue
刊名	Acta mathematica sinica-english series
	2007-11-01
卷号	23期号:11页码:2061-2068
关键词	Class group Redei matrix Reciprocity law
ISSN号	1439-8516
DOI	10.1007/s10114-007-0965-1
通讯作者	Xi mei wu(wuximei_81@126.com)
英文摘要	Let f = q(root-p(1)p(2)) be an imaginary quadratic field with distinct primes p(1) = p(2) = 1 mod 8 and the legendre symbol (p(1)/p(2)) = 1. then the 8-rank of the class group of f is equal to 2 if and only if the following conditions hold: (1) the quartic residue symbols (p(1)/p(2))4 = (p(1)/p(2))4 = 1; (2) either both p(1) and p(2) are represented by the form a(2) + 32b(2) over z and p(2)(h+(2p1)/4) = x(2) - 2p(1)y(2), x, y is an element of z, or both p(1) and p(2) are not represented by the form a(2) + 32b(2) over z and p(2)(h+(2p1)/4) = epsilon(2x(2) - p(1)y(2)), x, y is an element of z, epsilon is an element of {+/-1}, where h(+)(2p(1)) is the narrow class number of q(root 2p(1)). moreover, we also generalize these results.
WOS关键词	TAME KERNELS ; GAUSS SUM ; INDEX 4
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
语种	英语
出版者	SPRINGER HEIDELBERG
WOS记录号	WOS:000250481800012
内容类型	期刊论文
URI标识	http://www.corc.org.cn/handle/1471x/2380151
专题	中国科学院大学
通讯作者	Xi Mei Wu
作者单位	1.Nanjing Univ Aeronaut & Astronaut, Dept Math, Nanjing 210016, Peoples R China 2.Chinese Acad Sci, Grad Sch, State Key Lab Informat Secur, Beijing 100039, Peoples R China
推荐引用方式 GB/T 7714	Xi Mei Wu,Qin Yue. 8-ranks of class groups of some imaginary quadratic number fields[J]. Acta mathematica sinica-english series,2007,23(11):2061-2068.
APA	Xi Mei Wu,&Qin Yue.(2007).8-ranks of class groups of some imaginary quadratic number fields.Acta mathematica sinica-english series,23(11),2061-2068.
MLA	Xi Mei Wu,et al."8-ranks of class groups of some imaginary quadratic number fields".Acta mathematica sinica-english series 23.11(2007):2061-2068.

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