{"abstract":[{"text":"We determine the asymptotic growth of extensions of local function fields of characteristic p counted by discriminant, where the Galois group is a subgroup of the affine group AGL_1(p). More general, we solve the corresponding counting problems for all groups which arise in a tower of a cyclic extension of order p over a cyclic extension of degree d coprime to p. This in particular give answers for certain non-abelian groups including S_3, dihedral groups of order 2p, and many Frobenius groups.","lang":"eng"}],"status":"public","publication":"arXiv:2604.02152","type":"preprint","language":[{"iso":"eng"}],"external_id":{"arxiv":["2604.02152"]},"_id":"65358","user_id":"82981","year":"2026","citation":{"short":"J. Klüners, R. Müller, ArXiv:2604.02152 (2026).","bibtex":"@article{Klüners_Müller_2026, title={Counting Frobenius extensions over local function fields}, journal={arXiv:2604.02152}, author={Klüners, Jürgen and Müller, Raphael}, year={2026} }","mla":"Klüners, Jürgen, and Raphael Müller. “Counting Frobenius Extensions over Local Function Fields.” <i>ArXiv:2604.02152</i>, 2026.","apa":"Klüners, J., &#38; Müller, R. (2026). Counting Frobenius extensions over local function fields. In <i>arXiv:2604.02152</i>.","ama":"Klüners J, Müller R. Counting Frobenius extensions over local function fields. <i>arXiv:260402152</i>. Published online 2026.","chicago":"Klüners, Jürgen, and Raphael Müller. “Counting Frobenius Extensions over Local Function Fields.” <i>ArXiv:2604.02152</i>, 2026.","ieee":"J. Klüners and R. Müller, “Counting Frobenius extensions over local function fields,” <i>arXiv:2604.02152</i>. 2026."},"title":"Counting Frobenius extensions over local function fields","date_updated":"2026-04-07T08:14:45Z","date_created":"2026-04-07T08:13:59Z","author":[{"first_name":"Jürgen","last_name":"Klüners","id":"21202","full_name":"Klüners, Jürgen"},{"full_name":"Müller, Raphael","id":"55246","last_name":"Müller","first_name":"Raphael"}]}