Equidistribution for abelian extensions of global fields

2026/07/17 by Jiazhi He · 1 citation
#math.NT

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Abstract

We establish asymptotic formulas for abelian extensions of global function fields ordered by conductor and subject to prescribed local conditions. Our proof combines harmonic analysis with a theory of frobenian functions over global function fields developed in this paper. We interpret our result via equidistribution on algebraic stacks.

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• Multivariate counting of wild abelian extensions

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