For every global function field K and finite abelian p-group G, the multivariate generating function that counts sub-G-extensions by successive higher-ramification heights is rational.
Counting abelian extensions by A rtin- S chreier conductor
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Multivariate counting of wild abelian extensions
For every global function field K and finite abelian p-group G, the multivariate generating function that counts sub-G-extensions by successive higher-ramification heights is rational.