= Lower ramification filtration of a prime-power cyclotomic extension
{title2=$v_L(\sigma_a(\zeta-1)-(\zeta-1))=p^{v_p(a-1)}$}
For $L=\mathbb Q_p(\zeta_{p^n})$, the <uniformiser> $\zeta_{p^n}-1$ and the <uniformizer criterion for lower ramification groups> give the displayed <valuation> for $a\ne1$. Thus $G_0$ is the full unit group modulo $p^n$, and $G_i$ consists of units congruent to one modulo $p^j$ when $p^{j-1}\leq i\leq p^j-1$, $1\leq j<n$. All groups are trivial for $i\geq p^{n-1}$. The formula includes $p=2$, where the first congruence subgroup is already the full group.
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