Explicit uniformizers for certain totally ramified extensions of the field of $p$-adic numbers

Abstract

Let $p$ be an odd prime number. We construct explicit uniformizers for the totally ramified extension ${\mathbb{Q}}_p({\zeta }_{p^2},\sqrt[p]{p})$ of the field of $p$-adic numbers ${\mathbb{Q}}_p$, where ${\zeta }_{p^2}$ is a primitive $p^2$-th root of unity.

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