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

Research paper by Hugues Bellemare, Antonio Lei

Indexed on: 05 Dec '19Published on: 03 Dec '19Published in: arXiv - Mathematics - Number Theory

#### 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 field of $p$-adic numbers $\mathbb{Q}_p$, where $\zeta_{p^2}$ is a primitive $p^2$-th root of unity.