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Relating $p$-adic Valuations of Elements in $\mathbb{C}$ and $\mathbb{C}_p$
Let $K = \mathbb{Q}(\theta)$, where $\theta$ is a root of an irreducible polynomial $g \in \mathbb{Z}[t]$. Fix a rational prime $p$. Let $\theta^{(1)}, \ldots, \theta^{(n)}$ be the roots of $g$ in $\...
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