On the discriminant of pure number fields

Anuj Jakhar; Sudesh K. Khanduja; Neeraj Sangwan

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arXiv · 2005.01300

On the discriminant of pure number fields

Anuj Jakhar·Sudesh K. Khanduja·Neeraj Sangwan

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Abstract

Let $K=\mathbb{Q}(\sqrt[n]{a})$ be an extension of degree $n$ of the field $\Q$ 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 $a,n$.

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BibTeX RIS

Anuj Jakhar, Sudesh K. Khanduja, Neeraj Sangwan. 2020-05-04. On the discriminant of pure number fields. https://arxiv.org/abs/2005.01300

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