= Multiplicity of a place in a modulus
{title2=$m_v(\mathfrak c)$}
For a <modulus of a number field> $\mathfrak c=\mathfrak c_0\mathfrak c_\infty$, the multiplicity at a finite place is the exponent of its <prime ideal> in $\mathfrak c_0$. At a real <Archimedean place> it is one if that place occurs in $\mathfrak c_\infty$ and zero otherwise. Complex places have multiplicity zero. These effective modulus multiplicities encode congruences and positivity requirements in the <ray class group>.
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