@unpublished{66684,
  abstract     = {{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       = {{Gundlach, Fabian}},
  booktitle    = {{arXiv:2607.27364}},
  title        = {{{Multivariate counting of wild abelian extensions}}},
  year         = {{2026}},
}