论文标题
关于由三元素$ x^9+ax+b $定义的非IC数字字段的共同索引分隔线和单基因
On common index divisors and monogenity of of the nonic number field defined by a trinomial $x^9+ax+b$
论文作者
论文摘要
令$ k $为一个非IC数字字段，该字段由一个复杂的root $þ$生成的元素不可约的三项元素$ f（x）= x^9+ax+b \ in \ z [x] $，其中$ ab \ neq 0 $。令$ i（k）$为$ k $的索引。理性的Prime $ p $ dividing $ i（k）$称为$ k $的主要公共指数除数。在本文中，对于每一个理性的Prime $ p $，我们提供了必要的足够条件，具体仅取决于$ a $ a和$ b $，$ p $是$ k $的常见指数除数。作为我们结果的应用，我们确定了由这种三项官方定义的非发电性非IC数字字段的无限参数族。最后，给出了一些数字示例，说明了我们的理论结果。
Let $K $ be a nonic number field generated by a complex root $þ$ of a monic irreducible trinomial $ F(x)= x^9+ax+b \in \Z[x]$, where $ab \neq 0$. Let $i(K)$ be the index of $K$. A rational prime $p$ dividing $ i(K)$ is called a prime common index divisor of $K$. In this paper, for every rational prime $p$, we give necessary and sufficient conditions depending only $a$ and $b$ for which $p$ is a common index divisor of $K$. As application of our results we identify infinite parametric families of non-monogenic nonic numbers fields defined by such trinomials. At the end, some numerical examples illustrating our theoretical results are given.
