摘要
Suppose F = Q(√-p1 pt) is an imaginary quadratic number field with distinct primes p1,..., pt,where pi≡ 1(mod 4)(i = 1,..., t- 1) and pt ≡ 3(mod 4). We express the possible values of the 8-rank r8 of the class group of F in terms of a quadratic form Q over F2 which is defined by quartic symbols. In particular,we show that r8 is bounded by the isotropy index of Q.
Suppose F = Q（√-p1 pt） is an imaginary quadratic number field with distinct primes p1,..., pt,where pi≡ 1（mod 4）（i = 1,..., t- 1） and pt ≡ 3（mod 4）. We express the possible values of the 8-rank r8 of the class group of F in terms of a quadratic form Q over F2 which is defined by quartic symbols. In particular,we show that r8 is bounded by the isotropy index of Q.
基金
supported by China Postdoctoral Science Foundation(Grant No.2013M541064)
National Natural Science Foundation of China(Grant No.11371043)
National Basic Research Program of China(Grant No.2013CB834202)
