 Coleman norm operator

The determinant norm for the finite free extension $R/\phi (R)$ 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 $\mathcal{N}f=f$. For symmetric cyclotomic units, the product relation follows directly from ${\prod }_{{\xi }^p=1}(1-{\xi }^a{X}^a)=1-X^{ap}$ when $p\nmid a$.