= Lubin–Tate series
{c}
{title2=$f(T)$}
For a <uniformizer> $\pi$ of a non-Archimedean <local field> $K$ with <residue field> of cardinality $q$, a <Lubin–Tate series> is a series $f(T)\in\mathcal O_K[[T]]$ satisfying
$$
f(T)\equiv\pi T\pmod{T^2},\qquad f(T)\equiv T^q\pmod\pi.
$$
It determines the associated two-variable <Lubin–Tate formal group>. A useful example is $f(T)=\pi T+T^q$. For $K=\mathbb Q_p$ and $\pi=p$, the choice $(1+T)^p-1$ gives the <formal multiplicative group> and the <Lubin–Tate cyclotomic example>.
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