= CM period
{c}
{title2=$\Omega_\infty,\quad\Omega_p$}
A complex CM period compares an algebraic invariant differential on a <CM elliptic curve> with its analytic lattice coordinate. At an ordinary prime, a $p$-adic CM period compares the same differential with the invariant differential of the multiplicative formal group: an isomorphism $\eta$ is normalized by $\log_{\widehat E}\eta(T)=\Omega_p\log(1+T)$. Matched periods make normalized critical <Hecke L-function> values algebraic and give precise <p-adic L-function> interpolation.
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