= Ramification polynomial
{title2=$\rho_\pi(X)=f(\pi(1+X))/\pi^n$}
The ramification <polynomial> records the normalised differences of conjugates of a <uniformizer>, including the zero difference from the identity automorphism. Its quotient by $X$ is the <reduced ramification polynomial>. In the usual coefficient-index convention, the finite slopes of its lower <Newton polygon> are negatives of the <valuations> of its nonzero roots; the coefficient at the zero root is treated as having infinite <valuation>.
Back to article page
