{"user_id":"100450","language":[{"iso":"eng"}],"_id":"66684","date_updated":"2026-08-07T14:30:51Z","year":"2026","status":"public","title":"Multivariate counting of wild abelian extensions","author":[{"full_name":"Gundlach, Fabian","last_name":"Gundlach","first_name":"Fabian","id":"100450"}],"type":"preprint","external_id":{"arxiv":["2607.27364"]},"date_created":"2026-08-07T14:30:17Z","abstract":[{"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.","lang":"eng"}],"publication":"arXiv:2607.27364","citation":{"ieee":"F. Gundlach, “Multivariate counting of wild abelian extensions,” <i>arXiv:2607.27364</i>. 2026.","apa":"Gundlach, F. (2026). Multivariate counting of wild abelian extensions. In <i>arXiv:2607.27364</i>.","chicago":"Gundlach, Fabian. “Multivariate Counting of Wild Abelian Extensions.” <i>ArXiv:2607.27364</i>, 2026.","short":"F. Gundlach, ArXiv:2607.27364 (2026).","mla":"Gundlach, Fabian. “Multivariate Counting of Wild Abelian Extensions.” <i>ArXiv:2607.27364</i>, 2026.","bibtex":"@article{Gundlach_2026, title={Multivariate counting of wild abelian extensions}, journal={arXiv:2607.27364}, author={Gundlach, Fabian}, year={2026} }","ama":"Gundlach F. Multivariate counting of wild abelian extensions. <i>arXiv:260727364</i>. Published online 2026."}}