On the discriminant of pure number fields
Volume 167 / 2022
Colloquium Mathematicum 167 (2022), 149-157
MSC: 11R04, 11R29.
DOI: 10.4064/cm8257-11-2020
Published online: 24 May 2021
Abstract
Let $K=\mathbb {Q}(\sqrt [n]{a})$ be an extension of degree $n$ of the field $\mathbb Q $ of rational numbers, where the integer $a$ is such that for each prime $p$ dividing $n$ either $p\nmid a$ or the highest power of $p$ dividing $a$ is coprime to $p$; this condition is clearly satisfied when $a, n$ are coprime or $a$ is squarefree. The paper contains an explicit formula for the discriminant of $K$ involving only the prime powers dividing $a,n$.
