English

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}
}