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ON THE -RANK OF CLASS GROUPS OF DIRICHLET BIQUADRATIC FIELDS
Journal of the Institute of Mathematics of Jussieu ( IF 1.1 ) Pub Date : 2020-12-22 , DOI: 10.1017/s1474748020000651 Étienne Fouvry , Peter Koymans , Carlo Pagano
中文翻译:
关于狄利克利双二次域的类群的秩
更新日期:2020-12-22
Journal of the Institute of Mathematics of Jussieu ( IF 1.1 ) Pub Date : 2020-12-22 , DOI: 10.1017/s1474748020000651 Étienne Fouvry , Peter Koymans , Carlo Pagano
We show that for $100\%$ of the odd, square free integers $n> 0$ , the $4$ -rank of $\text {Cl}(\mathbb{Q} (i, \sqrt {n}))$ is equal to $\omega _3(n) - 1$ , where $\omega _3$ is the number of prime divisors of n that are $3$ modulo $4$ .
中文翻译:
关于狄利克利双二次域的类群的秩
我们证明对于 $100\%$ 的奇数、自由平方整数 $n> 0$ , $\text {Cl}(\mathbb{Q} (i, \sqrt {n}))$ 的 $4$ -rank等于 $\omega _3(n) - 1$ ,其中 $\omega _3$ 是n的素数除数数,它是 $3$ 模 $4$ 。