---
_id: '65358'
abstract:
- lang: eng
  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.
author:
- first_name: Jürgen
  full_name: Klüners, Jürgen
  id: '21202'
  last_name: Klüners
- first_name: Raphael
  full_name: Müller, Raphael
  id: '55246'
  last_name: Müller
citation:
  ama: Klüners J, Müller R. Counting Frobenius extensions over local function fields.
    <i>arXiv:260402152</i>. Published online 2026.
  apa: Klüners, J., &#38; Müller, R. (2026). Counting Frobenius extensions over local
    function fields. In <i>arXiv:2604.02152</i>.
  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} }'
  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.
  mla: Klüners, Jürgen, and Raphael Müller. “Counting Frobenius Extensions over Local
    Function Fields.” <i>ArXiv:2604.02152</i>, 2026.
  short: J. Klüners, R. Müller, ArXiv:2604.02152 (2026).
date_created: 2026-04-07T08:13:59Z
date_updated: 2026-04-07T08:14:45Z
external_id:
  arxiv:
  - '2604.02152'
language:
- iso: eng
publication: arXiv:2604.02152
status: public
title: Counting Frobenius extensions over local function fields
type: preprint
user_id: '82981'
year: '2026'
...