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

doi:10.1142/S1793042122500555

	Supersingular j-invariants and the class number of Q(root-p)
	Xiao, Guanju 1; Luo, Lixia 2,3; Deng, Yingpu 2,3
刊名	INTERNATIONAL JOURNAL OF NUMBER THEORY
	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
DOI	10.1142/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
出版者	WORLD SCIENTIFIC PUBL CO PTE LTD
WOS记录号	WOS:000804550500006
内容类型	期刊论文
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.