= Coleman norm operator
{c}
{title2=$\varphi(\mathcal Nf)=\prod_{\xi^p=1}f(\xi(1+T)-1)$}
The determinant norm for the finite free extension $R/\varphi(R)$ defines $\mathcal N$ on units. After adjoining the p-th <roots of unity>, the norm is the displayed product of conjugates. A <Coleman power series> of a norm-compatible unit sequence satisfies $\mathcal Nf=f$. For symmetric cyclotomic units, the product relation follows directly from $\prod_{\xi^p=1}(1-\xi^aX^a)=1-X^{ap}$ when $p\nmid a$.
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