On the Integral Representation of Binary Quadratic Forms and the Artin Condition

doi:10.3836/tjm/1502179249

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	On the Integral Representation of Binary Quadratic Forms and the Artin Condition
	Lv, Chang 4; Shentu, Junchao 5; Deng, Yingpu6,7
	2018-12-01
发表期刊	TOKYO JOURNAL OF MATHEMATICS
ISSN	0387-3870
卷号	41 期号:2 页码:371-384
摘要	For diophantine equations of the form ax(2) + bxy + cy(2) + g = 0 over Z whose coefficients satisfy some assumptions, we show that a condition with respect to the Artin reciprocity map, which we call the Artin condition, is the only obstruction to the local-global principle for integral solutions of the equation. Some concrete examples are presented.
关键词	binary quadratic forms integral points ring class field
DOI	10.3836/tjm/1502179249
语种	英语
资助项目	National Natural Science Foundation of China[11471314]
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000457878700003
出版者	TOKYO JOURNAL MATHEMATICS EDITORIAL OFFICE ACAD CENTER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/32432
专题	系统科学研究所
通讯作者	Lv, Chang
作者单位	1.Univ Sci & Technol China, Inst Informat Engn, CAS, Hefei, Anhui, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing, Peoples R China 3.Univ Chinese Acad Sci, Beijing, Peoples R China 4.Chinese Acad Sci, State Key Lab Informat Secur, Inst Informat Engn, Beijing 100093, Peoples R China 5.Univ Sci & Technol China, Hefei 230001, Anhui, Peoples R China 6.Univ Chinese Acad Sci, Key Lab Math Mechanizat, Acad Math & Syst Sci, Chinese Acad Sci,NCMIS, Beijing 100190, Peoples R China 7.Univ Chinese Acad Sci, Sch Math Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Lv, Chang,Shentu, Junchao,Deng, Yingpu. On the Integral Representation of Binary Quadratic Forms and the Artin Condition[J]. TOKYO JOURNAL OF MATHEMATICS,2018,41(2):371-384.
APA	Lv, Chang,Shentu, Junchao,&Deng, Yingpu.(2018).On the Integral Representation of Binary Quadratic Forms and the Artin Condition.TOKYO JOURNAL OF MATHEMATICS,41(2),371-384.
MLA	Lv, Chang,et al."On the Integral Representation of Binary Quadratic Forms and the Artin Condition".TOKYO JOURNAL OF MATHEMATICS 41.2(2018):371-384.