论文标题
$ x^7+ax^5+b $定义的化粪池字段的索引
The index of the septic number field defined by $x^7+ax^5+b$
论文作者
论文摘要
令$ k $为一个化粪池字段，该字段由一个不可约束的三元式$ f（x）= x^7+ax^5+b \ in \ z [x] $生成的复杂根$ $。令$ i（k）$为$ k $的索引。在本文中，我们表明$ i（k）\ in \ {1，2，4 \} $。以这种方式，我们回答了这些数字字段的narkiewicz \ cite {na}的问题$ 22 $。特别是，我们提供了足够的条件，$ k $是非单性的。我们通过一些计算示例来说明我们的结果。
Let $K $ be a septic number field generated by a complex root $þ$ of a monic irreducible trinomial $ F(x)= x^7+ax^5+b \in \Z[x]$. Let $i(K)$ be the index of $K$. In this paper, we show that $i(K) \in \{1, 2, 4\}$. In a such way, we answer to Problem $22$ of Narkiewicz \cite{Na} for these number fields. In particular, we provide sufficient conditions for which $K$ is non-monogenic. We illustrate our results by some computational examples.
