论文标题
多季度$ P $ - 合理的数字字段
Multi-quadratic $p$-rational Number Fields
论文作者
论文摘要
对于每个奇数$ p $，我们证明存在$ p $ - 理性的许多真实的二次字段。每个主要$ p $也给出了明确的虚构和真正的双方$ P $合理字段。 Using a recent method developed by Greenberg, we deduce the existence of Galois extensions of $\mathbf{Q}$ with Galois group isomorphic to an open subgroup of $GL_n(\mathbf{Z_p})$, for $n =4$ and $n =5$ and at least for all the primes $p <192.699.943$.
For each odd prime $p$, we prove the existence of infinitely many real quadratic fields which are $p$-rational. Explicit imaginary and real bi-quadratic $p$-rational fields are also given for each prime $p$. Using a recent method developed by Greenberg, we deduce the existence of Galois extensions of $\mathbf{Q}$ with Galois group isomorphic to an open subgroup of $GL_n(\mathbf{Z_p})$, for $n =4$ and $n =5$ and at least for all the primes $p <192.699.943$.
