---
_id: '42790'
abstract:
- lang: eng
  text: We show that exceptional algebraic groups over number fields do not admit
    one-class genera of parahoric groups, except in the case G₂ . For the group G₂,
    we enumerate all such one-class genera for the usual seven-dimensional representation.
author:
- first_name: Markus
  full_name: Kirschmer, Markus
  id: '82258'
  last_name: Kirschmer
citation:
  ama: Kirschmer M. One-class genera of exceptional groups over number fields. <i>Journal
    de Théorie des Nombres de Bordeaux</i>. 2018;30(3):847-857. doi:<a href="https://doi.org/10.5802/jtnb.1052">10.5802/jtnb.1052</a>
  apa: Kirschmer, M. (2018). One-class genera of exceptional groups over number fields.
    <i>Journal de Théorie Des Nombres de Bordeaux</i>, <i>30</i>(3), 847–857. <a href="https://doi.org/10.5802/jtnb.1052">https://doi.org/10.5802/jtnb.1052</a>
  bibtex: '@article{Kirschmer_2018, title={One-class genera of exceptional groups
    over number fields}, volume={30}, DOI={<a href="https://doi.org/10.5802/jtnb.1052">10.5802/jtnb.1052</a>},
    number={3}, journal={Journal de Théorie des Nombres de Bordeaux}, publisher={Cellule
    MathDoc/CEDRAM}, author={Kirschmer, Markus}, year={2018}, pages={847–857} }'
  chicago: 'Kirschmer, Markus. “One-Class Genera of Exceptional Groups over Number
    Fields.” <i>Journal de Théorie Des Nombres de Bordeaux</i> 30, no. 3 (2018): 847–57.
    <a href="https://doi.org/10.5802/jtnb.1052">https://doi.org/10.5802/jtnb.1052</a>.'
  ieee: 'M. Kirschmer, “One-class genera of exceptional groups over number fields,”
    <i>Journal de Théorie des Nombres de Bordeaux</i>, vol. 30, no. 3, pp. 847–857,
    2018, doi: <a href="https://doi.org/10.5802/jtnb.1052">10.5802/jtnb.1052</a>.'
  mla: Kirschmer, Markus. “One-Class Genera of Exceptional Groups over Number Fields.”
    <i>Journal de Théorie Des Nombres de Bordeaux</i>, vol. 30, no. 3, Cellule MathDoc/CEDRAM,
    2018, pp. 847–57, doi:<a href="https://doi.org/10.5802/jtnb.1052">10.5802/jtnb.1052</a>.
  short: M. Kirschmer, Journal de Théorie Des Nombres de Bordeaux 30 (2018) 847–857.
date_created: 2023-03-07T08:27:36Z
date_updated: 2023-04-04T09:07:32Z
department:
- _id: '102'
doi: 10.5802/jtnb.1052
extern: '1'
intvolume: '        30'
issue: '3'
keyword:
- Algebra and Number Theory
language:
- iso: eng
page: 847-857
publication: Journal de Théorie des Nombres de Bordeaux
publication_identifier:
  issn:
  - 1246-7405
  - 2118-8572
publication_status: published
publisher: Cellule MathDoc/CEDRAM
status: public
title: One-class genera of exceptional groups over number fields
type: journal_article
user_id: '93826'
volume: 30
year: '2018'
...
---
_id: '34889'
abstract:
- lang: eng
  text: We prove that van Hoeij’s original algorithm to factor univariate polynomials
    over the rationals runs in polynomial time, as well as natural variants. In particular,
    our approach also yields polynomial time complexity results for bivariate polynomials
    over a finite field.
author:
- first_name: Karim
  full_name: Belabas, Karim
  last_name: Belabas
- first_name: Mark
  full_name: van Hoeij, Mark
  last_name: van Hoeij
- first_name: Jürgen
  full_name: Klüners, Jürgen
  id: '21202'
  last_name: Klüners
- first_name: Allan
  full_name: Steel, Allan
  last_name: Steel
citation:
  ama: Belabas K, van Hoeij M, Klüners J, Steel A. Factoring polynomials over global
    fields. <i>Journal de Théorie des Nombres de Bordeaux</i>. 2009;21(1):15-39. doi:<a
    href="https://doi.org/10.5802/jtnb.655">10.5802/jtnb.655</a>
  apa: Belabas, K., van Hoeij, M., Klüners, J., &#38; Steel, A. (2009). Factoring
    polynomials over global fields. <i>Journal de Théorie Des Nombres de Bordeaux</i>,
    <i>21</i>(1), 15–39. <a href="https://doi.org/10.5802/jtnb.655">https://doi.org/10.5802/jtnb.655</a>
  bibtex: '@article{Belabas_van Hoeij_Klüners_Steel_2009, title={Factoring polynomials
    over global fields}, volume={21}, DOI={<a href="https://doi.org/10.5802/jtnb.655">10.5802/jtnb.655</a>},
    number={1}, journal={Journal de Théorie des Nombres de Bordeaux}, publisher={Cellule
    MathDoc/CEDRAM}, author={Belabas, Karim and van Hoeij, Mark and Klüners, Jürgen
    and Steel, Allan}, year={2009}, pages={15–39} }'
  chicago: 'Belabas, Karim, Mark van Hoeij, Jürgen Klüners, and Allan Steel. “Factoring
    Polynomials over Global Fields.” <i>Journal de Théorie Des Nombres de Bordeaux</i>
    21, no. 1 (2009): 15–39. <a href="https://doi.org/10.5802/jtnb.655">https://doi.org/10.5802/jtnb.655</a>.'
  ieee: 'K. Belabas, M. van Hoeij, J. Klüners, and A. Steel, “Factoring polynomials
    over global fields,” <i>Journal de Théorie des Nombres de Bordeaux</i>, vol. 21,
    no. 1, pp. 15–39, 2009, doi: <a href="https://doi.org/10.5802/jtnb.655">10.5802/jtnb.655</a>.'
  mla: Belabas, Karim, et al. “Factoring Polynomials over Global Fields.” <i>Journal
    de Théorie Des Nombres de Bordeaux</i>, vol. 21, no. 1, Cellule MathDoc/CEDRAM,
    2009, pp. 15–39, doi:<a href="https://doi.org/10.5802/jtnb.655">10.5802/jtnb.655</a>.
  short: K. Belabas, M. van Hoeij, J. Klüners, A. Steel, Journal de Théorie Des Nombres
    de Bordeaux 21 (2009) 15–39.
date_created: 2022-12-23T09:33:37Z
date_updated: 2023-03-06T09:09:56Z
department:
- _id: '102'
doi: 10.5802/jtnb.655
external_id:
  arxiv:
  - 'math/0409510 '
intvolume: '        21'
issue: '1'
keyword:
- Algebra and Number Theory
language:
- iso: eng
page: 15-39
publication: Journal de Théorie des Nombres de Bordeaux
publication_identifier:
  issn:
  - 1246-7405
publication_status: published
publisher: Cellule MathDoc/CEDRAM
status: public
title: Factoring polynomials over global fields
type: journal_article
user_id: '93826'
volume: 21
year: '2009'
...
---
_id: '34891'
abstract:
- lang: eng
  text: 'We study the asymptotics conjecture of Malle for dihedral groups Dℓ of order
    2ℓ, where ℓ is an odd prime. We prove the expected lower bound for those groups.
    For the upper bounds we show that there is a connection to class groups of quadratic
    number fields. The asymptotic behavior of those class groups is predicted by the
    Cohen--Lenstra heuristics. Under the assumption of this heuristic we are able
    to prove the expected upper bounds. '
author:
- first_name: Jürgen
  full_name: Klüners, Jürgen
  id: '21202'
  last_name: Klüners
citation:
  ama: Klüners J. Asymptotics of number fields and the Cohen–Lenstra heuristics. <i>Journal
    de Théorie des Nombres de Bordeaux</i>. 2006;18(3):607-615. doi:<a href="https://doi.org/10.5802/jtnb.561">10.5802/jtnb.561</a>
  apa: Klüners, J. (2006). Asymptotics of number fields and the Cohen–Lenstra heuristics.
    <i>Journal de Théorie Des Nombres de Bordeaux</i>, <i>18</i>(3), 607–615. <a href="https://doi.org/10.5802/jtnb.561">https://doi.org/10.5802/jtnb.561</a>
  bibtex: '@article{Klüners_2006, title={Asymptotics of number fields and the Cohen–Lenstra
    heuristics}, volume={18}, DOI={<a href="https://doi.org/10.5802/jtnb.561">10.5802/jtnb.561</a>},
    number={3}, journal={Journal de Théorie des Nombres de Bordeaux}, publisher={Cellule
    MathDoc/CEDRAM}, author={Klüners, Jürgen}, year={2006}, pages={607–615} }'
  chicago: 'Klüners, Jürgen. “Asymptotics of Number Fields and the Cohen–Lenstra Heuristics.”
    <i>Journal de Théorie Des Nombres de Bordeaux</i> 18, no. 3 (2006): 607–15. <a
    href="https://doi.org/10.5802/jtnb.561">https://doi.org/10.5802/jtnb.561</a>.'
  ieee: 'J. Klüners, “Asymptotics of number fields and the Cohen–Lenstra heuristics,”
    <i>Journal de Théorie des Nombres de Bordeaux</i>, vol. 18, no. 3, pp. 607–615,
    2006, doi: <a href="https://doi.org/10.5802/jtnb.561">10.5802/jtnb.561</a>.'
  mla: Klüners, Jürgen. “Asymptotics of Number Fields and the Cohen–Lenstra Heuristics.”
    <i>Journal de Théorie Des Nombres de Bordeaux</i>, vol. 18, no. 3, Cellule MathDoc/CEDRAM,
    2006, pp. 607–15, doi:<a href="https://doi.org/10.5802/jtnb.561">10.5802/jtnb.561</a>.
  short: J. Klüners, Journal de Théorie Des Nombres de Bordeaux 18 (2006) 607–615.
date_created: 2022-12-23T09:37:01Z
date_updated: 2023-03-06T09:12:04Z
department:
- _id: '102'
doi: 10.5802/jtnb.561
external_id:
  arxiv:
  - 'math/0512260 '
intvolume: '        18'
issue: '3'
keyword:
- Algebra and Number Theory
language:
- iso: eng
page: 607-615
publication: Journal de Théorie des Nombres de Bordeaux
publication_identifier:
  issn:
  - 1246-7405
publication_status: published
publisher: Cellule MathDoc/CEDRAM
status: public
title: Asymptotics of number fields and the Cohen–Lenstra heuristics
type: journal_article
user_id: '93826'
volume: 18
year: '2006'
...