Counting abelian number fields with restricted ramification type

Julie Tavernier

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arXiv · 2507.00448

Counting abelian number fields with restricted ramification type

Julie Tavernier

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Abstract

We count abelian number fields ordered by arbitrary height function whose generator of tame inertia is restricted to lie in a given subset of the Galois group, and find an explicit formula for the leading constant. We interpret our results as a version of the Batyrev-Manin conjecture on $BG$ and rephrase our result on number fields with restricted ramification type in terms of integral points on $BG$. We also prove that such number fields are equidistributed with respect to suitable collections of infinitely many local conditions.

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Julie Tavernier. 2025-07-01. Counting abelian number fields with restricted ramification type. https://arxiv.org/abs/2507.00448

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