On orders in number fields: Picard groups, ring class fields and applications

doi:10.1007/s11425-015-4979-3

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	On orders in number fields: Picard groups, ring class fields and applications
	Lv Chang; Deng YingPu
刊名	SCIENCE CHINA-MATHEMATICS
	2015-08-01
卷号	58 期号:8 页码:1627-1638
关键词	orders Picard groups ring class fields integral points
ISSN号	1674-7283
DOI	10.1007/s11425-015-4979-3
英文摘要	We focus on orders in arbitrary number fields, consider their Picard groups and finally obtain ring class fields corresponding to them. The Galois group of the ring class field is isomorphic to the Picard group. As an application, we give criteria of the integral solvability of the diophantine equation p = x (2) + ny (2) over a class of imaginary quadratic fields where p is a prime element.
资助项目	National Natural Science Foundation of China[11471314] ; National Basic Research Program of China (973 Project)[2011CB302401] ; National Center for Mathematics and Interdisciplinary Sciences, Chinese Academy of Sciences
WOS研究方向	Mathematics
语种	英语
出版者	SCIENCE PRESS
WOS记录号	WOS:000358172300004
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/20412]
专题	系统科学研究所
通讯作者	Lv Chang
作者单位	Chinese Acad Sci, Acad Math & Syst Sci, NCMIS, Key Lab Math Mechanizat, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Lv Chang,Deng YingPu. On orders in number fields: Picard groups, ring class fields and applications[J]. SCIENCE CHINA-MATHEMATICS,2015,58(8):1627-1638.
APA	Lv Chang,&Deng YingPu.(2015).On orders in number fields: Picard groups, ring class fields and applications.SCIENCE CHINA-MATHEMATICS,58(8),1627-1638.
MLA	Lv Chang,et al."On orders in number fields: Picard groups, ring class fields and applications".SCIENCE CHINA-MATHEMATICS 58.8(2015):1627-1638.