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On the Integral Representation of Binary Quadratic Forms and the Artin Condition
Lv, Chang4; Shentu, Junchao5; Deng, Yingpu6,7
2018-12-01
Source PublicationTOKYO JOURNAL OF MATHEMATICS
ISSN0387-3870
Volume41Issue:2Pages:371-384
AbstractFor 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.
Keywordbinary quadratic forms integral points ring class field
DOI10.3836/tjm/1502179249
Language英语
Funding ProjectNational Natural Science Foundation of China[11471314]
WOS Research AreaMathematics
WOS SubjectMathematics
WOS IDWOS:000457878700003
PublisherTOKYO JOURNAL MATHEMATICS EDITORIAL OFFICE ACAD CENTER
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/32432
Collection系统科学研究所
Affiliation1.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
Recommended Citation
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.
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