关于Dirichlet双二次域

IF 0.3 4区数学 Q4 MATHEMATICS

Journal De Theorie Des Nombres De Bordeaux Pub Date : 2020-01-15 DOI:10.5802/jtnb.1220

'Etienne Fouvry, P. Koymans

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引用次数: 3

摘要

我们研究了$K_n := \mathbb{Q}(\sqrt{-n}, \sqrt{n})$的理想类群的$4$ -秩。我们的主要结果是，对于一个正比例的无平方整数$n$，我们有$\text{Cl}(K_n)$的$4$ -秩等于$\omega_3(n) - 1$，其中$\omega_3(n)$是$n$的质因数的个数$3$模$4$。

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On Dirichlet biquadratic fields

We study the $4$-rank of the ideal class group of $K_n := \mathbb{Q}(\sqrt{-n}, \sqrt{n})$. Our main result is that for a positive proportion of the squarefree integers $n$ we have that the $4$-rank of $\text{Cl}(K_n)$ equals $\omega_3(n) - 1$, where $\omega_3(n)$ is the number of prime divisors of $n$ that are $3$ modulo $4$.

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来源期刊

Journal De Theorie Des Nombres De Bordeaux MATHEMATICS-

CiteScore

0.60

自引率

0.00%

发文量

期刊介绍： The Journal de Théorie des Nombres de Bordeaux publishes original papers on number theory and related topics (not published elsewhere).