8-rank of the class group and isotropy index
Lu Qing1,2
AbstractSuppose is an imaginary quadratic number field with distinct primes p (1), aEuro broken vertical bar, p (t) , where p (i) a parts per thousand 1 (mod 4) (i = 1, aEuro broken vertical bar, t - 1) and p (t) a parts per thousand 3 (mod 4). We express the possible values of the 8-rank r (8) of the class group of F in terms of a quadratic form Q over which is defined by quartic symbols. In particular, we show that r (8) is bounded by the isotropy index of Q.
Keywordimaginary quadratic field class group 8-rank isotropy index Redei matrix
Funding ProjectChina Postdoctoral Science Foundation[2013M541064] ; National Natural Science Foundation of China[11371043] ; National Basic Research Program of China[2013CB834202]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000355824300004
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Document Type期刊论文
Corresponding AuthorLu Qing
Affiliation1.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
Recommended Citation
GB/T 7714
Lu Qing. 8-rank of the class group and isotropy index[J]. SCIENCE CHINA-MATHEMATICS,2015,58(7):1433-1444.
APA Lu Qing.(2015).8-rank of the class group and isotropy index.SCIENCE CHINA-MATHEMATICS,58(7),1433-1444.
MLA Lu Qing."8-rank of the class group and isotropy index".SCIENCE CHINA-MATHEMATICS 58.7(2015):1433-1444.
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