{"date_updated":"2025-01-15T11:37:28Z","year":"2024","status":"public","date_created":"2025-01-15T11:37:13Z","publication":"arXiv:2410.23964","type":"preprint","title":"Counting abelian extensions by Artin-Schreier conductor","external_id":{"arxiv":["2410.23964"]},"citation":{"ieee":"F. Gundlach, “Counting abelian extensions by Artin-Schreier conductor,” <i>arXiv:2410.23964</i>. 2024.","mla":"Gundlach, Fabian. “Counting Abelian Extensions by Artin-Schreier Conductor.” <i>ArXiv:2410.23964</i>, 2024.","chicago":"Gundlach, Fabian. “Counting Abelian Extensions by Artin-Schreier Conductor.” <i>ArXiv:2410.23964</i>, 2024.","bibtex":"@article{Gundlach_2024, title={Counting abelian extensions by Artin-Schreier conductor}, journal={arXiv:2410.23964}, author={Gundlach, Fabian}, year={2024} }","ama":"Gundlach F. Counting abelian extensions by Artin-Schreier conductor. <i>arXiv:241023964</i>. Published online 2024.","short":"F. Gundlach, ArXiv:2410.23964 (2024).","apa":"Gundlach, F. (2024). Counting abelian extensions by Artin-Schreier conductor. In <i>arXiv:2410.23964</i>."},"abstract":[{"lang":"eng","text":"Let $G$ be a finite abelian $p$-group. We count $G$-extensions of global\r\nrational function fields $\\mathbb F_q(T)$ of characteristic $p$ by the degree\r\nof what we call their Artin-Schreier conductor. The corresponding (ordinary)\r\ngenerating function turns out to be rational. This gives an exact answer to the\r\ncounting problem, and seems to beg for a geometric interpretation.\r\n  This is in contrast with the generating functions for the ordinary conductor\r\n(from class field theory) and the discriminant, which in general have no\r\nmeromorphic continuation to the entire complex plane."}],"author":[{"id":"100450","last_name":"Gundlach","full_name":"Gundlach, Fabian","first_name":"Fabian"}],"user_id":"100450","_id":"58191","language":[{"iso":"eng"}]}