On power integral bases of certain pure number fields defined by $x^{3^r\cdot 7^s}-m$

Abstract

Let $K$ be a pure number field generated by a complex root of a monic irreducible polynomial $F(x)=x^{3^r\cdot 7^s}-m\in \mathbb {Z}[x]$ with $m\neq \pm 1$ a square free integer, and $r$ and $s$ two positive integers. In this paper, we study the monogenei