论文标题
$ \ mathbb {q} _p $的假泰特曲线扩展的统一器
Uniformizer of the False Tate Curve Extension of $\mathbb{Q}_p$
论文作者
论文摘要
令$ p \ geq 3 $为素数。在本文中，我们研究了原始$ p^n $ - unity $ζ_{p^n} $的规范扩展，in $ p $ -adic mal'cev-neumann field $ \ mathbb {l} _p $ for $ n \ geq for $ n \ geq 1 $。更准确地说，我们为第一个$ \ aleph_0 $的显式公式提供了$ζ_{p^n} $的术语，并且作为一个应用程序，我们使用它来构造$ k_ {2，m} = \ mathbb {q} Q} _p {q} _p \ p^p^$ q p^2}，p^2}，p^2}，p^2}，p^2}，p^2}，p^2}， $ M \ GEQ 1 $。
Let $p\geq 3$ be a prime number. In this article, we study the canonical expansion of the primitive $p^n$-th root of unity $ζ_{p^n}$ in $p$-adic Mal'cev-Neumann field $\mathbb{L}_p$ for $n\geq 1$. More precisely, we give the explicit formula for the first $\aleph_0$ terms of the expansion of $ζ_{p^n}$ and as an application, we use it to construct a uniformizer of $K_{2,m}=\mathbb{Q}_p\left(ζ_{p^2},p^{1/p^m}\right)$ with $m\geq 1$.
