Equidistribution for abelian extensions of global fields
Number Theory
2026-07-17 v1
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.
Cite
@article{arxiv.2607.16079,
title = {Equidistribution for abelian extensions of global fields},
author = {Jiazhi He},
journal= {arXiv preprint arXiv:2607.16079},
year = {2026}
}