preprint Fabian Gundlach author 100450 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. 2026 eng 2607.27364 Gundlach, F. (2026). Multivariate counting of wild abelian extensions. In <i>arXiv:2607.27364</i>. F. Gundlach, “Multivariate counting of wild abelian extensions,” <i>arXiv:2607.27364</i>. 2026. Gundlach, Fabian. “Multivariate Counting of Wild Abelian Extensions.” <i>ArXiv:2607.27364</i>, 2026. F. Gundlach, ArXiv:2607.27364 (2026). Gundlach, Fabian. “Multivariate Counting of Wild Abelian Extensions.” <i>ArXiv:2607.27364</i>, 2026. Gundlach F. Multivariate counting of wild abelian extensions. <i>arXiv:260727364</i>. Published online 2026. @article{Gundlach_2026, title={Multivariate counting of wild abelian extensions}, journal={arXiv:2607.27364}, author={Gundlach, Fabian}, year={2026} } 666842026-08-07T14:30:17Z2026-08-07T14:30:51Z