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Supersingular j-invariants and the class number of Q(root-p)

文献类型：期刊论文

作者Xiao, Guanju1; Luo, Lixia2,3; Deng, Yingpu2,3
刊名INTERNATIONAL JOURNAL OF NUMBER THEORY
出版日期2022-06-01
卷号18期号:05页码:1065-1078
关键词Supersingular j-invariants class polynomials class number imaginary quadratic order
ISSN号1793-0421
DOI10.1142/S1793042122500555
英文摘要Let p > 3 be a prime. Let D be the discriminant of an imaginary quadratic order. Assume that vertical bar D vertical bar < 4 root p/3 and (D/p) = - 1. We compute the number of F-p-roots of the class polynomials H-D(X). Suppose Q(root D-1) not equal Q(root D-2), we prove that two class polynomials H-D1 (X) and H-D2 (X) have a common root in F-p if and only if D-1 D-2 - 4p is a perfect square. Furthermore, any three class polynomials do not have a common root in F-p. As an application, we propose a deterministic algorithm for computing the class number of Q(root-p).
资助项目National Key R&D Program of China[2020YFA0712300]
WOS研究方向Mathematics
语种英语
WOS记录号WOS:000804550500006
出版者WORLD SCIENTIFIC PUBL CO PTE LTD
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/61424]  
专题中国科学院数学与系统科学研究院
通讯作者Xiao, Guanju
作者单位1.Natl Univ Def Technol, Coll Liberal Arts & Sci, Changsha 410073, Peoples R China
2.Chinese Acad Sci, Acad Math & Syst Sci, Key Lab Math Mechanizat, NCMIS, Beijing 100190, Peoples R China
3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
推荐引用方式
GB/T 7714		 Xiao, Guanju,Luo, Lixia,Deng, Yingpu. Supersingular j-invariants and the class number of Q(root-p)[J]. INTERNATIONAL JOURNAL OF NUMBER THEORY,2022,18(05):1065-1078.
APA Xiao, Guanju,Luo, Lixia,&Deng, Yingpu.(2022).Supersingular j-invariants and the class number of Q(root-p).INTERNATIONAL JOURNAL OF NUMBER THEORY,18(05),1065-1078.
MLA Xiao, Guanju,et al."Supersingular j-invariants and the class number of Q(root-p)".INTERNATIONAL JOURNAL OF NUMBER THEORY 18.05(2022):1065-1078.

入库方式： OAI收割

来源：数学与系统科学研究院

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