---
_id: '66684'
abstract:
- lang: eng
  text: Let $K$ be a global function field of characteristic~$p$ and let $G$ be a
    finite abelian group of exponent $p^e$. We show that the multivariate generating
    function counting sub-$G$-extensions of $K$ with respect to $e$ specific height
    functions (encoding successive drops in the exponents of the higher ramification
    groups) is rational.
author:
- first_name: Fabian
  full_name: Gundlach, Fabian
  id: '100450'
  last_name: Gundlach
citation:
  ama: Gundlach F. Multivariate counting of wild abelian extensions. <i>arXiv:260727364</i>.
    Published online 2026.
  apa: Gundlach, F. (2026). Multivariate counting of wild abelian extensions. In <i>arXiv:2607.27364</i>.
  bibtex: '@article{Gundlach_2026, title={Multivariate counting of wild abelian extensions},
    journal={arXiv:2607.27364}, author={Gundlach, Fabian}, year={2026} }'
  chicago: Gundlach, Fabian. “Multivariate Counting of Wild Abelian Extensions.” <i>ArXiv:2607.27364</i>,
    2026.
  ieee: F. Gundlach, “Multivariate counting of wild abelian extensions,” <i>arXiv:2607.27364</i>.
    2026.
  mla: Gundlach, Fabian. “Multivariate Counting of Wild Abelian Extensions.” <i>ArXiv:2607.27364</i>,
    2026.
  short: F. Gundlach, ArXiv:2607.27364 (2026).
date_created: 2026-08-07T14:30:17Z
date_updated: 2026-08-07T14:30:51Z
external_id:
  arxiv:
  - '2607.27364'
language:
- iso: eng
publication: arXiv:2607.27364
status: public
title: Multivariate counting of wild abelian extensions
type: preprint
user_id: '100450'
year: '2026'
...