---
_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'
...
---
_id: '59990'
author:
- first_name: Andreas
  full_name: Eichler, Andreas
  last_name: Eichler
- first_name: Henrik
  full_name: Floren, Henrik
  last_name: Floren
- first_name: Irene
  full_name: Garnelo Abellanas, Irene
  id: '93843'
  last_name: Garnelo Abellanas
- first_name: Michael
  full_name: Liebendörfer, Michael
  id: '30933'
  last_name: Liebendörfer
  orcid: 0000-0001-9887-2074
- first_name: Raphael
  full_name: Müller, Raphael
  id: '55246'
  last_name: Müller
- first_name: Mirko
  full_name: Schürmann, Mirko
  id: '59707'
  last_name: Schürmann
  orcid: 0000-0003-2646-085X
- first_name: Annabelle
  full_name: Speer, Annabelle
  last_name: Speer
citation:
  ama: 'Eichler A, Floren H, Garnelo Abellanas I, et al. Digital STACK tasks and exam
    results. In: <i>INDRUM2024 PROCEEDINGS Fifth Conference of the International Network
    for Didactic Research in University Mathematics</i>. Escola Univerist`aria Salesiana
    de Sarri`a – Univ. Aut`onoma de Barcelona and INDRUM; 2024. doi:<a href="https://theses.hal.science/INDRUM2024/hal-04944194v1">https://theses.hal.science/INDRUM2024/hal-04944194v1</a>'
  apa: Eichler, A., Floren, H., Garnelo Abellanas, I., Liebendörfer, M., Müller, R.,
    Schürmann, M., &#38; Speer, A. (2024). Digital STACK tasks and exam results. <i>INDRUM2024
    PROCEEDINGS Fifth Conference of the International Network for Didactic Research
    in University Mathematics</i>. Fifth conference of the International Network for
    Didactic Research in University Mathematics, Barcelona. <a href="https://theses.hal.science/INDRUM2024/hal-04944194v1">https://theses.hal.science/INDRUM2024/hal-04944194v1</a>
  bibtex: '@inproceedings{Eichler_Floren_Garnelo Abellanas_Liebendörfer_Müller_Schürmann_Speer_2024,
    place={Barcelona}, title={Digital STACK tasks and exam results}, DOI={<a href="https://theses.hal.science/INDRUM2024/hal-04944194v1">https://theses.hal.science/INDRUM2024/hal-04944194v1</a>},
    booktitle={INDRUM2024 PROCEEDINGS Fifth conference of the International Network
    for Didactic Research in University Mathematics}, publisher={Escola Univerist`aria
    Salesiana de Sarri`a – Univ. Aut`onoma de Barcelona and INDRUM}, author={Eichler,
    Andreas and Floren, Henrik and Garnelo Abellanas, Irene and Liebendörfer, Michael
    and Müller, Raphael and Schürmann, Mirko and Speer, Annabelle}, year={2024} }'
  chicago: 'Eichler, Andreas, Henrik Floren, Irene Garnelo Abellanas, Michael Liebendörfer,
    Raphael Müller, Mirko Schürmann, and Annabelle Speer. “Digital STACK Tasks and
    Exam Results.” In <i>INDRUM2024 PROCEEDINGS Fifth Conference of the International
    Network for Didactic Research in University Mathematics</i>. Barcelona: Escola
    Univerist`aria Salesiana de Sarri`a – Univ. Aut`onoma de Barcelona and INDRUM,
    2024. <a href="https://theses.hal.science/INDRUM2024/hal-04944194v1">https://theses.hal.science/INDRUM2024/hal-04944194v1</a>.'
  ieee: 'A. Eichler <i>et al.</i>, “Digital STACK tasks and exam results,” presented
    at the Fifth conference of the International Network for Didactic Research in
    University Mathematics, Barcelona, 2024, doi: <a href="https://theses.hal.science/INDRUM2024/hal-04944194v1">https://theses.hal.science/INDRUM2024/hal-04944194v1</a>.'
  mla: Eichler, Andreas, et al. “Digital STACK Tasks and Exam Results.” <i>INDRUM2024
    PROCEEDINGS Fifth Conference of the International Network for Didactic Research
    in University Mathematics</i>, Escola Univerist`aria Salesiana de Sarri`a – Univ.
    Aut`onoma de Barcelona and INDRUM, 2024, doi:<a href="https://theses.hal.science/INDRUM2024/hal-04944194v1">https://theses.hal.science/INDRUM2024/hal-04944194v1</a>.
  short: 'A. Eichler, H. Floren, I. Garnelo Abellanas, M. Liebendörfer, R. Müller,
    M. Schürmann, A. Speer, in: INDRUM2024 PROCEEDINGS Fifth Conference of the International
    Network for Didactic Research in University Mathematics, Escola Univerist`aria
    Salesiana de Sarri`a – Univ. Aut`onoma de Barcelona and INDRUM, Barcelona, 2024.'
conference:
  end_date: 2024-06-14
  location: Barcelona
  name: Fifth conference of the International Network for Didactic Research in University
    Mathematics
  start_date: 2024-06-10
date_created: 2025-05-19T08:51:27Z
date_updated: 2025-06-25T07:50:49Z
ddc:
- '510'
doi: https://theses.hal.science/INDRUM2024/hal-04944194v1
file:
- access_level: open_access
  content_type: application/pdf
  creator: rmuelle2
  date_created: 2025-05-19T08:51:19Z
  date_updated: 2025-05-19T08:51:19Z
  file_id: '59991'
  file_name: Poster_Indrum_2024_Digital-STACK-Tasks_Exam-Results.pdf
  file_size: 850253
  relation: main_file
file_date_updated: 2025-05-19T08:51:19Z
has_accepted_license: '1'
language:
- iso: eng
main_file_link:
- url: https://theses.hal.science/INDRUM2024/hal-04944194v1
oa: '1'
place: Barcelona
publication: INDRUM2024 PROCEEDINGS Fifth conference of the International Network
  for Didactic Research in University Mathematics
publication_identifier:
  issn:
  - 2496-1027 (online)
publication_status: published
publisher: Escola Univerist`aria Salesiana de Sarri`a – Univ. Aut`onoma de Barcelona
  and INDRUM
status: public
title: Digital STACK tasks and exam results
type: conference
user_id: '55246'
year: '2024'
...
---
_id: '59988'
author:
- first_name: Raphael
  full_name: Müller, Raphael
  id: '55246'
  last_name: Müller
citation:
  ama: Müller R. <i>On the Asymptotics of Wildly Ramified Local Function Field Extensions</i>.;
    2023.
  apa: Müller, R. (2023). <i>On the asymptotics of wildly ramified local function
    field extensions</i>.
  bibtex: '@book{Müller_2023, title={On the asymptotics of wildly ramified local function
    field extensions}, author={Müller, Raphael}, year={2023} }'
  chicago: Müller, Raphael. <i>On the Asymptotics of Wildly Ramified Local Function
    Field Extensions</i>, 2023.
  ieee: R. Müller, <i>On the asymptotics of wildly ramified local function field extensions</i>.
    2023.
  mla: Müller, Raphael. <i>On the Asymptotics of Wildly Ramified Local Function Field
    Extensions</i>. 2023.
  short: R. Müller, On the Asymptotics of Wildly Ramified Local Function Field Extensions,
    2023.
date_created: 2025-05-19T08:22:06Z
date_updated: 2025-05-19T08:58:21Z
department:
- _id: '43'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://katalog.ub.uni-paderborn.de/local/r/99372717691706441
oa: '1'
publication_status: published
status: public
title: On the asymptotics of wildly ramified local function field extensions
type: dissertation
user_id: '55246'
year: '2023'
...
---
_id: '59989'
author:
- first_name: Raphael
  full_name: Müller, Raphael
  id: '55246'
  last_name: Müller
- first_name: Jürgen
  full_name: Klüners, Jürgen
  last_name: Klüners
citation:
  ama: Müller R, Klüners J. The conductor density of local function fields with abelian
    Galois group. <i>Journal of Number Theory</i>. 2020;212.
  apa: Müller, R., &#38; Klüners, J. (2020). The conductor density of local function
    fields with abelian Galois group. <i>Journal of Number Theory</i>, <i>212</i>.
  bibtex: '@article{Müller_Klüners_2020, title={The conductor density of local function
    fields with abelian Galois group}, volume={212}, journal={Journal of Number Theory},
    author={Müller, Raphael and Klüners, Jürgen}, year={2020} }'
  chicago: Müller, Raphael, and Jürgen Klüners. “The Conductor Density of Local Function
    Fields with Abelian Galois Group.” <i>Journal of Number Theory</i> 212 (2020).
  ieee: R. Müller and J. Klüners, “The conductor density of local function fields
    with abelian Galois group,” <i>Journal of Number Theory</i>, vol. 212, 2020.
  mla: Müller, Raphael, and Jürgen Klüners. “The Conductor Density of Local Function
    Fields with Abelian Galois Group.” <i>Journal of Number Theory</i>, vol. 212,
    2020.
  short: R. Müller, J. Klüners, Journal of Number Theory 212 (2020).
date_created: 2025-05-19T08:31:53Z
date_updated: 2025-06-13T08:15:14Z
department:
- _id: '43'
intvolume: '       212'
language:
- iso: eng
publication: Journal of Number Theory
related_material:
  link:
  - relation: earlier_version
    url: https://arxiv.org/abs/1904.02573
status: public
title: The conductor density of local function fields with abelian Galois group
type: journal_article
user_id: '82981'
volume: 212
year: '2020'
...