= Cyclotomic higher logarithmic derivative
{title2=$\delta_k(u)=\left.D^{k-1}(Df_u/f_u)\right|_{T=0},\quad D=(1+T)d/dT$}
= Higher logarithmic derivative
{synonym}
For a norm-compatible sequence of local units, its <Coleman power series> $f_u\in\mathbb Z_p[[T]]^\times$ defines these integral additive homomorphisms. In the formal coordinate $z=\log(1+T)$ they are the derivatives of $\log f_u(e^z-1)$; the constant term of the logarithm is irrelevant. A Galois element with cyclotomic value $a$ multiplies the kth derivative by $a^k$. This is the multiplicative-formal-group version of the <Coates–Wiles homomorphism>.
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