---
_id: '34835'
abstract:
- lang: eng
  text: 'We prove an upper bound for the asymptotics of counting functions of number
    fields with nilpotent Galois groups. '
author:
- first_name: Jürgen
  full_name: Klüners, Jürgen
  id: '21202'
  last_name: Klüners
citation:
  ama: Klüners J. The asymptotics of nilpotent Galois groups. <i>Acta Arithmetica</i>.
    2022;204(2):165-184. doi:<a href="https://doi.org/10.4064/aa211207-16-5">10.4064/aa211207-16-5</a>
  apa: Klüners, J. (2022). The asymptotics of nilpotent Galois groups. <i>Acta Arithmetica</i>,
    <i>204</i>(2), 165–184. <a href="https://doi.org/10.4064/aa211207-16-5">https://doi.org/10.4064/aa211207-16-5</a>
  bibtex: '@article{Klüners_2022, title={The asymptotics of nilpotent Galois groups},
    volume={204}, DOI={<a href="https://doi.org/10.4064/aa211207-16-5">10.4064/aa211207-16-5</a>},
    number={2}, journal={Acta Arithmetica}, publisher={Institute of Mathematics, Polish
    Academy of Sciences}, author={Klüners, Jürgen}, year={2022}, pages={165–184} }'
  chicago: 'Klüners, Jürgen. “The Asymptotics of Nilpotent Galois Groups.” <i>Acta
    Arithmetica</i> 204, no. 2 (2022): 165–84. <a href="https://doi.org/10.4064/aa211207-16-5">https://doi.org/10.4064/aa211207-16-5</a>.'
  ieee: 'J. Klüners, “The asymptotics of nilpotent Galois groups,” <i>Acta Arithmetica</i>,
    vol. 204, no. 2, pp. 165–184, 2022, doi: <a href="https://doi.org/10.4064/aa211207-16-5">10.4064/aa211207-16-5</a>.'
  mla: Klüners, Jürgen. “The Asymptotics of Nilpotent Galois Groups.” <i>Acta Arithmetica</i>,
    vol. 204, no. 2, Institute of Mathematics, Polish Academy of Sciences, 2022, pp.
    165–84, doi:<a href="https://doi.org/10.4064/aa211207-16-5">10.4064/aa211207-16-5</a>.
  short: J. Klüners, Acta Arithmetica 204 (2022) 165–184.
date_created: 2022-12-22T10:08:23Z
date_updated: 2023-03-06T08:48:33Z
department:
- _id: '102'
doi: 10.4064/aa211207-16-5
external_id:
  arxiv:
  - '2011.04325 '
intvolume: '       204'
issue: '2'
keyword:
- Algebra and Number Theory
language:
- iso: eng
page: 165-184
publication: Acta Arithmetica
publication_identifier:
  issn:
  - 0065-1036
  - 1730-6264
publication_status: published
publisher: Institute of Mathematics, Polish Academy of Sciences
status: public
title: The asymptotics of nilpotent Galois groups
type: journal_article
user_id: '93826'
volume: 204
year: '2022'
...
---
_id: '34842'
abstract:
- lang: eng
  text: Let D<0 be a fundamental discriminant and denote by E(D) the exponent of the
    ideal class group Cl(D) of K=ℚ(√D). Under the assumption that no Siegel zeros
    exist we compute all such D with E(D) dividing 8. We compute all D with |D| ≤
    3.1⋅10²⁰ such that E(D) ≤ 8.
author:
- first_name: Andreas-Stephan
  full_name: Elsenhans, Andreas-Stephan
  last_name: Elsenhans
- first_name: Jürgen
  full_name: Klüners, Jürgen
  id: '21202'
  last_name: Klüners
- first_name: Florin
  full_name: Nicolae, Florin
  last_name: Nicolae
citation:
  ama: Elsenhans A-S, Klüners J, Nicolae F. Imaginary quadratic number fields with
    class groups of small exponent. <i>Acta Arithmetica</i>. 2020;193(3):217-233.
    doi:<a href="https://doi.org/10.4064/aa180220-20-3">10.4064/aa180220-20-3</a>
  apa: Elsenhans, A.-S., Klüners, J., &#38; Nicolae, F. (2020). Imaginary quadratic
    number fields with class groups of small exponent. <i>Acta Arithmetica</i>, <i>193</i>(3),
    217–233. <a href="https://doi.org/10.4064/aa180220-20-3">https://doi.org/10.4064/aa180220-20-3</a>
  bibtex: '@article{Elsenhans_Klüners_Nicolae_2020, title={Imaginary quadratic number
    fields with class groups of small exponent}, volume={193}, DOI={<a href="https://doi.org/10.4064/aa180220-20-3">10.4064/aa180220-20-3</a>},
    number={3}, journal={Acta Arithmetica}, publisher={Institute of Mathematics, Polish
    Academy of Sciences}, author={Elsenhans, Andreas-Stephan and Klüners, Jürgen and
    Nicolae, Florin}, year={2020}, pages={217–233} }'
  chicago: 'Elsenhans, Andreas-Stephan, Jürgen Klüners, and Florin Nicolae. “Imaginary
    Quadratic Number Fields with Class Groups of Small Exponent.” <i>Acta Arithmetica</i>
    193, no. 3 (2020): 217–33. <a href="https://doi.org/10.4064/aa180220-20-3">https://doi.org/10.4064/aa180220-20-3</a>.'
  ieee: 'A.-S. Elsenhans, J. Klüners, and F. Nicolae, “Imaginary quadratic number
    fields with class groups of small exponent,” <i>Acta Arithmetica</i>, vol. 193,
    no. 3, pp. 217–233, 2020, doi: <a href="https://doi.org/10.4064/aa180220-20-3">10.4064/aa180220-20-3</a>.'
  mla: Elsenhans, Andreas-Stephan, et al. “Imaginary Quadratic Number Fields with
    Class Groups of Small Exponent.” <i>Acta Arithmetica</i>, vol. 193, no. 3, Institute
    of Mathematics, Polish Academy of Sciences, 2020, pp. 217–33, doi:<a href="https://doi.org/10.4064/aa180220-20-3">10.4064/aa180220-20-3</a>.
  short: A.-S. Elsenhans, J. Klüners, F. Nicolae, Acta Arithmetica 193 (2020) 217–233.
date_created: 2022-12-22T10:51:13Z
date_updated: 2023-03-06T10:19:53Z
department:
- _id: '102'
doi: 10.4064/aa180220-20-3
external_id:
  arxiv:
  - '1803.02056 '
intvolume: '       193'
issue: '3'
keyword:
- Algebra and Number Theory
language:
- iso: eng
page: 217-233
publication: Acta Arithmetica
publication_identifier:
  issn:
  - 0065-1036
  - 1730-6264
publication_status: published
publisher: Institute of Mathematics, Polish Academy of Sciences
status: public
title: Imaginary quadratic number fields with class groups of small exponent
type: journal_article
user_id: '93826'
volume: 193
year: '2020'
...
---
_id: '34892'
abstract:
- lang: eng
  text: 'We prove that the number of quartic S4--extensions of the rationals of given
    discriminant d is $O_\eps(d^{1/2+\eps})$ for all $\eps>0$. For a prime number
    p we derive that the dimension of the space of octahedral modular forms of weight
    1 and conductor p or p² is bounded above by O(p¹/²log(p)²). '
author:
- first_name: Jürgen
  full_name: Klüners, Jürgen
  id: '21202'
  last_name: Klüners
citation:
  ama: Klüners J. The number of S₄-fields with given discriminant. <i>Acta Arithmetica</i>.
    2006;122(2):185-194. doi:<a href="https://doi.org/10.4064/aa122-2-3">10.4064/aa122-2-3</a>
  apa: Klüners, J. (2006). The number of S₄-fields with given discriminant. <i>Acta
    Arithmetica</i>, <i>122</i>(2), 185–194. <a href="https://doi.org/10.4064/aa122-2-3">https://doi.org/10.4064/aa122-2-3</a>
  bibtex: '@article{Klüners_2006, title={The number of S₄-fields with given discriminant},
    volume={122}, DOI={<a href="https://doi.org/10.4064/aa122-2-3">10.4064/aa122-2-3</a>},
    number={2}, journal={Acta Arithmetica}, publisher={Institute of Mathematics, Polish
    Academy of Sciences}, author={Klüners, Jürgen}, year={2006}, pages={185–194} }'
  chicago: 'Klüners, Jürgen. “The Number of S₄-Fields with given Discriminant.” <i>Acta
    Arithmetica</i> 122, no. 2 (2006): 185–94. <a href="https://doi.org/10.4064/aa122-2-3">https://doi.org/10.4064/aa122-2-3</a>.'
  ieee: 'J. Klüners, “The number of S₄-fields with given discriminant,” <i>Acta Arithmetica</i>,
    vol. 122, no. 2, pp. 185–194, 2006, doi: <a href="https://doi.org/10.4064/aa122-2-3">10.4064/aa122-2-3</a>.'
  mla: Klüners, Jürgen. “The Number of S₄-Fields with given Discriminant.” <i>Acta
    Arithmetica</i>, vol. 122, no. 2, Institute of Mathematics, Polish Academy of
    Sciences, 2006, pp. 185–94, doi:<a href="https://doi.org/10.4064/aa122-2-3">10.4064/aa122-2-3</a>.
  short: J. Klüners, Acta Arithmetica 122 (2006) 185–194.
date_created: 2022-12-23T09:40:25Z
date_updated: 2023-03-06T09:52:41Z
department:
- _id: '102'
doi: 10.4064/aa122-2-3
external_id:
  arxiv:
  - math/0411484
intvolume: '       122'
issue: '2'
keyword:
- Algebra and Number Theory
language:
- iso: eng
page: 185-194
publication: Acta Arithmetica
publication_identifier:
  issn:
  - 0065-1036
  - 1730-6264
publication_status: published
publisher: Institute of Mathematics, Polish Academy of Sciences
status: public
title: The number of S₄-fields with given discriminant
type: journal_article
user_id: '93826'
volume: 122
year: '2006'
...