For any finite abelian group G and global function field k, G-extensions with conductor q^M and prescribed local conditions satisfy an explicit asymptotic q^{aM} M^{b-1}, with local equidistribution governed by a Tamagawa measure.
Frei and Loughran, D
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Equidistribution for abelian extensions of global fields
For any finite abelian group G and global function field k, G-extensions with conductor q^M and prescribed local conditions satisfy an explicit asymptotic q^{aM} M^{b-1}, with local equidistribution governed by a Tamagawa measure.