8-ranks of class groups of quadratic number fields and their densities
8-ranks of class groups of quadratic number fields and their densities
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DOI：
10.1007/s10114-011-8273-1
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发表时间：
2011-06
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影响因子：
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通讯作者：
Q. Yue
中科院分区：
文献类型：
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作者：
Q. Yue
对于ɛ∈{±1，±2}，素数−p≡q≡1 mod 4，我们给出了F的8阶窄类群等于1或2的充要条件，从而可以计算它们的密度.所有结果都用p，q模2n，四次剩余符号和二元二次型的同余关系表示，如qh(−2p)/4=x2+2py2，其中h(−2p)是的类数。所得结果对数值计算是非常有用的。
For,ɛ∈ {±1, ±2}, primes −p≡q≡ 1 mod 4, we give the necessary and sufficient conditions for 8-ranks of narrow class groups ofFequal to 1 or 2 such that we can calculate their densities. All results are stated in terms of congruence relations ofp, qmodulo 2n, the quartic residue symboland binary quadratic forms such asqh(−2p)/4=x2+ 2py2, whereh(−2p) is the class number of. The results are very useful for numerical computations.