---
_id: '55276'
author:
- first_name: P.
  full_name: Minelli, P.
  last_name: Minelli
- first_name: A.
  full_name: Sourmelidis, A.
  last_name: Sourmelidis
- first_name: Marc
  full_name: Technau, Marc
  id: '106108'
  last_name: Technau
  orcid: 0000-0001-9650-2459
citation:
  ama: Minelli P, Sourmelidis A, Technau M. On restricted averages of Dedekind sums.
    <i>Int Math Res Not IMRN</i>. 2024;2024(10):8485–8502. doi:<a href="https://doi.org/10.1093/imrn/rnad283">10.1093/imrn/rnad283</a>
  apa: Minelli, P., Sourmelidis, A., &#38; Technau, M. (2024). On restricted averages
    of Dedekind sums. <i>Int. Math. Res. Not. IMRN</i>, <i>2024</i>(10), 8485–8502.
    <a href="https://doi.org/10.1093/imrn/rnad283">https://doi.org/10.1093/imrn/rnad283</a>
  bibtex: '@article{Minelli_Sourmelidis_Technau_2024, title={On restricted averages
    of Dedekind sums}, volume={2024}, DOI={<a href="https://doi.org/10.1093/imrn/rnad283">10.1093/imrn/rnad283</a>},
    number={10}, journal={Int. Math. Res. Not. IMRN}, author={Minelli, P. and Sourmelidis,
    A. and Technau, Marc}, year={2024}, pages={8485–8502} }'
  chicago: 'Minelli, P., A. Sourmelidis, and Marc Technau. “On Restricted Averages
    of Dedekind Sums.” <i>Int. Math. Res. Not. IMRN</i> 2024, no. 10 (2024): 8485–8502.
    <a href="https://doi.org/10.1093/imrn/rnad283">https://doi.org/10.1093/imrn/rnad283</a>.'
  ieee: 'P. Minelli, A. Sourmelidis, and M. Technau, “On restricted averages of Dedekind
    sums,” <i>Int. Math. Res. Not. IMRN</i>, vol. 2024, no. 10, pp. 8485–8502, 2024,
    doi: <a href="https://doi.org/10.1093/imrn/rnad283">10.1093/imrn/rnad283</a>.'
  mla: Minelli, P., et al. “On Restricted Averages of Dedekind Sums.” <i>Int. Math.
    Res. Not. IMRN</i>, vol. 2024, no. 10, 2024, pp. 8485–8502, doi:<a href="https://doi.org/10.1093/imrn/rnad283">10.1093/imrn/rnad283</a>.
  short: P. Minelli, A. Sourmelidis, M. Technau, Int. Math. Res. Not. IMRN 2024 (2024)
    8485–8502.
date_created: 2024-07-16T11:09:00Z
date_updated: 2024-07-24T07:23:20Z
department:
- _id: '102'
doi: 10.1093/imrn/rnad283
intvolume: '      2024'
issue: '10'
language:
- iso: eng
page: 8485–8502
publication: Int. Math. Res. Not. IMRN
status: public
title: On restricted averages of Dedekind sums
type: journal_article
user_id: '106108'
volume: 2024
year: '2024'
...
---
_id: '55278'
author:
- first_name: Marc
  full_name: Technau, Marc
  id: '106108'
  last_name: Technau
  orcid: 0000-0001-9650-2459
citation:
  ama: Technau M. Remark on the Farey fraction spin chain. <i>Proc Amer Math Soc</i>.
    2024;152(1):63–69. doi:<a href="https://doi.org/10.1090/proc/16520">10.1090/proc/16520</a>
  apa: Technau, M. (2024). Remark on the Farey fraction spin chain. <i>Proc. Amer.
    Math. Soc.</i>, <i>152</i>(1), 63–69. <a href="https://doi.org/10.1090/proc/16520">https://doi.org/10.1090/proc/16520</a>
  bibtex: '@article{Technau_2024, title={Remark on the Farey fraction spin chain},
    volume={152}, DOI={<a href="https://doi.org/10.1090/proc/16520">10.1090/proc/16520</a>},
    number={1}, journal={Proc. Amer. Math. Soc.}, author={Technau, Marc}, year={2024},
    pages={63–69} }'
  chicago: 'Technau, Marc. “Remark on the Farey Fraction Spin Chain.” <i>Proc. Amer.
    Math. Soc.</i> 152, no. 1 (2024): 63–69. <a href="https://doi.org/10.1090/proc/16520">https://doi.org/10.1090/proc/16520</a>.'
  ieee: 'M. Technau, “Remark on the Farey fraction spin chain,” <i>Proc. Amer. Math.
    Soc.</i>, vol. 152, no. 1, pp. 63–69, 2024, doi: <a href="https://doi.org/10.1090/proc/16520">10.1090/proc/16520</a>.'
  mla: Technau, Marc. “Remark on the Farey Fraction Spin Chain.” <i>Proc. Amer. Math.
    Soc.</i>, vol. 152, no. 1, 2024, pp. 63–69, doi:<a href="https://doi.org/10.1090/proc/16520">10.1090/proc/16520</a>.
  short: M. Technau, Proc. Amer. Math. Soc. 152 (2024) 63–69.
date_created: 2024-07-16T11:09:01Z
date_updated: 2024-07-24T07:26:12Z
department:
- _id: '102'
doi: 10.1090/proc/16520
extern: '1'
intvolume: '       152'
issue: '1'
language:
- iso: eng
page: 63–69
publication: Proc. Amer. Math. Soc.
status: public
title: Remark on the Farey fraction spin chain
type: journal_article
user_id: '106108'
volume: 152
year: '2024'
...
---
_id: '49372'
author:
- first_name: Jürgen
  full_name: Klüners, Jürgen
  id: '21202'
  last_name: Klüners
- first_name: Jiuya
  full_name: Wang, Jiuya
  last_name: Wang
citation:
  ama: Klüners J, Wang J. Idélic Approach in Enumerating Heisenberg Extensions. <i>La
    Matematica</i>. Published online 2023. doi:<a href="https://doi.org/10.1007/s44007-023-00067-w">10.1007/s44007-023-00067-w</a>
  apa: Klüners, J., &#38; Wang, J. (2023). Idélic Approach in Enumerating Heisenberg
    Extensions. <i>La Matematica</i>. <a href="https://doi.org/10.1007/s44007-023-00067-w">https://doi.org/10.1007/s44007-023-00067-w</a>
  bibtex: '@article{Klüners_Wang_2023, title={Idélic Approach in Enumerating Heisenberg
    Extensions}, DOI={<a href="https://doi.org/10.1007/s44007-023-00067-w">10.1007/s44007-023-00067-w</a>},
    journal={La Matematica}, publisher={Springer Science and Business Media LLC},
    author={Klüners, Jürgen and Wang, Jiuya}, year={2023} }'
  chicago: Klüners, Jürgen, and Jiuya Wang. “Idélic Approach in Enumerating Heisenberg
    Extensions.” <i>La Matematica</i>, 2023. <a href="https://doi.org/10.1007/s44007-023-00067-w">https://doi.org/10.1007/s44007-023-00067-w</a>.
  ieee: 'J. Klüners and J. Wang, “Idélic Approach in Enumerating Heisenberg Extensions,”
    <i>La Matematica</i>, 2023, doi: <a href="https://doi.org/10.1007/s44007-023-00067-w">10.1007/s44007-023-00067-w</a>.'
  mla: Klüners, Jürgen, and Jiuya Wang. “Idélic Approach in Enumerating Heisenberg
    Extensions.” <i>La Matematica</i>, Springer Science and Business Media LLC, 2023,
    doi:<a href="https://doi.org/10.1007/s44007-023-00067-w">10.1007/s44007-023-00067-w</a>.
  short: J. Klüners, J. Wang, La Matematica (2023).
date_created: 2023-12-01T09:23:59Z
date_updated: 2023-12-06T09:50:43Z
department:
- _id: '102'
doi: 10.1007/s44007-023-00067-w
language:
- iso: eng
publication: La Matematica
publication_identifier:
  issn:
  - 2730-9657
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Idélic Approach in Enumerating Heisenberg Extensions
type: journal_article
user_id: '21202'
year: '2023'
...
---
_id: '55277'
author:
- first_name: B.
  full_name: Klahn, B.
  last_name: Klahn
- first_name: Marc
  full_name: Technau, Marc
  id: '106108'
  last_name: Technau
  orcid: 0000-0001-9650-2459
citation:
  ama: Klahn B, Technau M. Galois groups of (<sup>n</sup>₀)+(<sup>n</sup>₁)X+…+(<sup>n</sup>₆)X<sup>6</sup>.
    <i>Int J Number Theory</i>. 2023;19(10):2443–2450. doi:<a href="https://doi.org/10.1142/S1793042123501208">10.1142/S1793042123501208</a>
  apa: Klahn, B., &#38; Technau, M. (2023). Galois groups of (<sup>n</sup>₀)+(<sup>n</sup>₁)X+…+(<sup>n</sup>₆)X<sup>6</sup>.
    <i>Int. J. Number Theory</i>, <i>19</i>(10), 2443–2450. <a href="https://doi.org/10.1142/S1793042123501208">https://doi.org/10.1142/S1793042123501208</a>
  bibtex: '@article{Klahn_Technau_2023, title={Galois groups of (<sup>n</sup>₀)+(<sup>n</sup>₁)X+…+(<sup>n</sup>₆)X<sup>6</sup>},
    volume={19}, DOI={<a href="https://doi.org/10.1142/S1793042123501208">10.1142/S1793042123501208</a>},
    number={10}, journal={Int. J. Number Theory}, author={Klahn, B. and Technau, Marc},
    year={2023}, pages={2443–2450} }'
  chicago: 'Klahn, B., and Marc Technau. “Galois Groups of (<sup>n</sup>₀)+(<sup>n</sup>₁)X+…+(<sup>n</sup>₆)X<sup>6</sup>.”
    <i>Int. J. Number Theory</i> 19, no. 10 (2023): 2443–2450. <a href="https://doi.org/10.1142/S1793042123501208">https://doi.org/10.1142/S1793042123501208</a>.'
  ieee: 'B. Klahn and M. Technau, “Galois groups of (<sup>n</sup>₀)+(<sup>n</sup>₁)X+…+(<sup>n</sup>₆)X<sup>6</sup>,”
    <i>Int. J. Number Theory</i>, vol. 19, no. 10, pp. 2443–2450, 2023, doi: <a href="https://doi.org/10.1142/S1793042123501208">10.1142/S1793042123501208</a>.'
  mla: Klahn, B., and Marc Technau. “Galois Groups of (<sup>n</sup>₀)+(<sup>n</sup>₁)X+…+(<sup>n</sup>₆)X<sup>6</sup>.”
    <i>Int. J. Number Theory</i>, vol. 19, no. 10, 2023, pp. 2443–2450, doi:<a href="https://doi.org/10.1142/S1793042123501208">10.1142/S1793042123501208</a>.
  short: B. Klahn, M. Technau, Int. J. Number Theory 19 (2023) 2443–2450.
date_created: 2024-07-16T11:09:01Z
date_updated: 2024-07-24T07:23:33Z
department:
- _id: '102'
doi: 10.1142/S1793042123501208
extern: '1'
intvolume: '        19'
issue: '10'
language:
- iso: eng
page: 2443–2450
publication: Int. J. Number Theory
status: public
title: Galois groups of (ⁿ₀)+(ⁿ₁)X+…+(ⁿ₆)X⁶
type: journal_article
user_id: '106108'
volume: 19
year: '2023'
...
---
_id: '55279'
author:
- first_name: P.
  full_name: Minelli, P.
  last_name: Minelli
- first_name: A.
  full_name: Sourmelidis, A.
  last_name: Sourmelidis
- first_name: Marc
  full_name: Technau, Marc
  id: '106108'
  last_name: Technau
  orcid: 0000-0001-9650-2459
citation:
  ama: Minelli P, Sourmelidis A, Technau M. Bias in the number of steps in the Euclidean
    algorithm and a conjecture of Ito on Dedekind sums. <i>Math Ann</i>. 2023;387:291–320.
    doi:<a href="https://doi.org/10.1007/s00208-022-02452-2">10.1007/s00208-022-02452-2</a>
  apa: Minelli, P., Sourmelidis, A., &#38; Technau, M. (2023). Bias in the number
    of steps in the Euclidean algorithm and a conjecture of Ito on Dedekind sums.
    <i>Math. Ann.</i>, <i>387</i>, 291–320. <a href="https://doi.org/10.1007/s00208-022-02452-2">https://doi.org/10.1007/s00208-022-02452-2</a>
  bibtex: '@article{Minelli_Sourmelidis_Technau_2023, title={Bias in the number of
    steps in the Euclidean algorithm and a conjecture of Ito on Dedekind sums}, volume={387},
    DOI={<a href="https://doi.org/10.1007/s00208-022-02452-2">10.1007/s00208-022-02452-2</a>},
    journal={Math. Ann.}, author={Minelli, P. and Sourmelidis, A. and Technau, Marc},
    year={2023}, pages={291–320} }'
  chicago: 'Minelli, P., A. Sourmelidis, and Marc Technau. “Bias in the Number of
    Steps in the Euclidean Algorithm and a Conjecture of Ito on Dedekind Sums.” <i>Math.
    Ann.</i> 387 (2023): 291–320. <a href="https://doi.org/10.1007/s00208-022-02452-2">https://doi.org/10.1007/s00208-022-02452-2</a>.'
  ieee: 'P. Minelli, A. Sourmelidis, and M. Technau, “Bias in the number of steps
    in the Euclidean algorithm and a conjecture of Ito on Dedekind sums,” <i>Math.
    Ann.</i>, vol. 387, pp. 291–320, 2023, doi: <a href="https://doi.org/10.1007/s00208-022-02452-2">10.1007/s00208-022-02452-2</a>.'
  mla: Minelli, P., et al. “Bias in the Number of Steps in the Euclidean Algorithm
    and a Conjecture of Ito on Dedekind Sums.” <i>Math. Ann.</i>, vol. 387, 2023,
    pp. 291–320, doi:<a href="https://doi.org/10.1007/s00208-022-02452-2">10.1007/s00208-022-02452-2</a>.
  short: P. Minelli, A. Sourmelidis, M. Technau, Math. Ann. 387 (2023) 291–320.
date_created: 2024-07-16T11:09:01Z
date_updated: 2024-07-24T07:26:05Z
department:
- _id: '102'
doi: 10.1007/s00208-022-02452-2
extern: '1'
intvolume: '       387'
language:
- iso: eng
page: 291–320
publication: Math. Ann.
status: public
title: Bias in the number of steps in the Euclidean algorithm and a conjecture of
  Ito on Dedekind sums
type: journal_article
user_id: '106108'
volume: 387
year: '2023'
...
---
_id: '55280'
author:
- first_name: Ch.
  full_name: Elsholtz, Ch.
  last_name: Elsholtz
- first_name: B.
  full_name: Klahn, B.
  last_name: Klahn
- first_name: Marc
  full_name: Technau, Marc
  id: '106108'
  last_name: Technau
  orcid: 0000-0001-9650-2459
citation:
  ama: Elsholtz Ch, Klahn B, Technau M. On polynomials with roots modulo almost all
    primes. <i>Acta Arith</i>. 2022;205:3(3):251–263. doi:<a href="https://doi.org/10.4064/aa220407-9-7">10.4064/aa220407-9-7</a>
  apa: Elsholtz, Ch., Klahn, B., &#38; Technau, M. (2022). On polynomials with roots
    modulo almost all primes. <i>Acta Arith.</i>, <i>205:3</i>(3), 251–263. <a href="https://doi.org/10.4064/aa220407-9-7">https://doi.org/10.4064/aa220407-9-7</a>
  bibtex: '@article{Elsholtz_Klahn_Technau_2022, title={On polynomials with roots
    modulo almost all primes}, volume={205:3}, DOI={<a href="https://doi.org/10.4064/aa220407-9-7">10.4064/aa220407-9-7</a>},
    number={3}, journal={Acta Arith.}, author={Elsholtz, Ch. and Klahn, B. and Technau,
    Marc}, year={2022}, pages={251–263} }'
  chicago: 'Elsholtz, Ch., B. Klahn, and Marc Technau. “On Polynomials with Roots
    modulo Almost All Primes.” <i>Acta Arith.</i> 205:3, no. 3 (2022): 251–263. <a
    href="https://doi.org/10.4064/aa220407-9-7">https://doi.org/10.4064/aa220407-9-7</a>.'
  ieee: 'Ch. Elsholtz, B. Klahn, and M. Technau, “On polynomials with roots modulo
    almost all primes,” <i>Acta Arith.</i>, vol. 205:3, no. 3, pp. 251–263, 2022,
    doi: <a href="https://doi.org/10.4064/aa220407-9-7">10.4064/aa220407-9-7</a>.'
  mla: Elsholtz, Ch., et al. “On Polynomials with Roots modulo Almost All Primes.”
    <i>Acta Arith.</i>, vol. 205:3, no. 3, 2022, pp. 251–263, doi:<a href="https://doi.org/10.4064/aa220407-9-7">10.4064/aa220407-9-7</a>.
  short: Ch. Elsholtz, B. Klahn, M. Technau, Acta Arith. 205:3 (2022) 251–263.
date_created: 2024-07-16T11:09:01Z
date_updated: 2024-07-24T07:26:22Z
department:
- _id: '102'
doi: 10.4064/aa220407-9-7
extern: '1'
issue: '3'
language:
- iso: eng
page: 251–263
publication: Acta Arith.
status: public
title: On polynomials with roots modulo almost all primes
type: journal_article
user_id: '106108'
volume: 205:3
year: '2022'
...
---
_id: '34839'
abstract:
- lang: eng
  text: We describe the relations among the ℓ-torsion conjecture, a conjecture of
    Malle giving an upper bound for the number of extensions, and the discriminant
    multiplicity conjecture. We prove that the latter two conjectures are equivalent
    in some sense. Altogether, the three conjectures are equivalent for the class
    of solvable groups. We then prove the ℓ-torsion conjecture for ℓ-groups and the
    other two conjectures for nilpotent groups.
author:
- first_name: Jürgen
  full_name: Klüners, Jürgen
  id: '21202'
  last_name: Klüners
- first_name: Jiuya
  full_name: Wang, Jiuya
  last_name: Wang
citation:
  ama: Klüners J, Wang J. ℓ-torsion bounds for the class group of number fields with
    an ℓ-group as Galois group. <i>Proceedings of the American Mathematical Society</i>.
    2022;150(7):2793-2805. doi:<a href="https://doi.org/10.1090/proc/15882">10.1090/proc/15882</a>
  apa: Klüners, J., &#38; Wang, J. (2022). ℓ-torsion bounds for the class group of
    number fields with an ℓ-group as Galois group. <i>Proceedings of the American
    Mathematical Society</i>, <i>150</i>(7), 2793–2805. <a href="https://doi.org/10.1090/proc/15882">https://doi.org/10.1090/proc/15882</a>
  bibtex: '@article{Klüners_Wang_2022, title={ℓ-torsion bounds for the class group
    of number fields with an ℓ-group as Galois group}, volume={150}, DOI={<a href="https://doi.org/10.1090/proc/15882">10.1090/proc/15882</a>},
    number={7}, journal={Proceedings of the American Mathematical Society}, publisher={American
    Mathematical Society (AMS)}, author={Klüners, Jürgen and Wang, Jiuya}, year={2022},
    pages={2793–2805} }'
  chicago: 'Klüners, Jürgen, and Jiuya Wang. “ℓ-Torsion Bounds for the Class Group
    of Number Fields with an ℓ-Group as Galois Group.” <i>Proceedings of the American
    Mathematical Society</i> 150, no. 7 (2022): 2793–2805. <a href="https://doi.org/10.1090/proc/15882">https://doi.org/10.1090/proc/15882</a>.'
  ieee: 'J. Klüners and J. Wang, “ℓ-torsion bounds for the class group of number fields
    with an ℓ-group as Galois group,” <i>Proceedings of the American Mathematical
    Society</i>, vol. 150, no. 7, pp. 2793–2805, 2022, doi: <a href="https://doi.org/10.1090/proc/15882">10.1090/proc/15882</a>.'
  mla: Klüners, Jürgen, and Jiuya Wang. “ℓ-Torsion Bounds for the Class Group of Number
    Fields with an ℓ-Group as Galois Group.” <i>Proceedings of the American Mathematical
    Society</i>, vol. 150, no. 7, American Mathematical Society (AMS), 2022, pp. 2793–805,
    doi:<a href="https://doi.org/10.1090/proc/15882">10.1090/proc/15882</a>.
  short: J. Klüners, J. Wang, Proceedings of the American Mathematical Society 150
    (2022) 2793–2805.
date_created: 2022-12-22T10:47:01Z
date_updated: 2023-03-06T08:47:42Z
department:
- _id: '102'
doi: 10.1090/proc/15882
external_id:
  arxiv:
  - '2003.12161 '
intvolume: '       150'
issue: '7'
keyword:
- Applied Mathematics
- General Mathematics
language:
- iso: eng
page: 2793-2805
publication: Proceedings of the American Mathematical Society
publication_identifier:
  issn:
  - 0002-9939
  - 1088-6826
publication_status: published
publisher: American Mathematical Society (AMS)
status: public
title: ℓ-torsion bounds for the class group of number fields with an ℓ-group as Galois
  group
type: journal_article
user_id: '93826'
volume: 150
year: '2022'
...
---
_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: '45854'
abstract:
- lang: eng
  text: In a previous paper the authors developed an algorithm to classify certain
    quaternary quadratic lattices over totally real fields. The present article applies
    this algorithm to the classification of binary Hermitian lattices over totally
    imaginary fields. We use it in particular to classify the 48-dimensional extremal
    even unimodular lattices over the integers that admit a semilarge automorphism.
author:
- first_name: Markus
  full_name: Kirschmer, Markus
  id: '82258'
  last_name: Kirschmer
- first_name: Gabriele
  full_name: Nebe, Gabriele
  last_name: Nebe
citation:
  ama: Kirschmer M, Nebe G. Binary Hermitian Lattices over Number Fields. <i>Experimental
    Mathematics</i>. 2022;31(1):280-301. doi:<a href="https://doi.org/10.1080/10586458.2019.1618756">10.1080/10586458.2019.1618756</a>
  apa: Kirschmer, M., &#38; Nebe, G. (2022). Binary Hermitian Lattices over Number
    Fields. <i>Experimental Mathematics</i>, <i>31</i>(1), 280–301. <a href="https://doi.org/10.1080/10586458.2019.1618756">https://doi.org/10.1080/10586458.2019.1618756</a>
  bibtex: '@article{Kirschmer_Nebe_2022, title={Binary Hermitian Lattices over Number
    Fields}, volume={31}, DOI={<a href="https://doi.org/10.1080/10586458.2019.1618756">10.1080/10586458.2019.1618756</a>},
    number={1}, journal={Experimental Mathematics}, publisher={Informa UK Limited},
    author={Kirschmer, Markus and Nebe, Gabriele}, year={2022}, pages={280–301} }'
  chicago: 'Kirschmer, Markus, and Gabriele Nebe. “Binary Hermitian Lattices over
    Number Fields.” <i>Experimental Mathematics</i> 31, no. 1 (2022): 280–301. <a
    href="https://doi.org/10.1080/10586458.2019.1618756">https://doi.org/10.1080/10586458.2019.1618756</a>.'
  ieee: 'M. Kirschmer and G. Nebe, “Binary Hermitian Lattices over Number Fields,”
    <i>Experimental Mathematics</i>, vol. 31, no. 1, pp. 280–301, 2022, doi: <a href="https://doi.org/10.1080/10586458.2019.1618756">10.1080/10586458.2019.1618756</a>.'
  mla: Kirschmer, Markus, and Gabriele Nebe. “Binary Hermitian Lattices over Number
    Fields.” <i>Experimental Mathematics</i>, vol. 31, no. 1, Informa UK Limited,
    2022, pp. 280–301, doi:<a href="https://doi.org/10.1080/10586458.2019.1618756">10.1080/10586458.2019.1618756</a>.
  short: M. Kirschmer, G. Nebe, Experimental Mathematics 31 (2022) 280–301.
date_created: 2023-07-04T08:28:04Z
date_updated: 2023-07-04T08:29:22Z
department:
- _id: '102'
doi: 10.1080/10586458.2019.1618756
intvolume: '        31'
issue: '1'
keyword:
- General Mathematics
language:
- iso: eng
page: 280-301
publication: Experimental Mathematics
publication_identifier:
  issn:
  - 1058-6458
  - 1944-950X
publication_status: published
publisher: Informa UK Limited
status: public
title: Binary Hermitian Lattices over Number Fields
type: journal_article
user_id: '93826'
volume: 31
year: '2022'
...
---
_id: '55290'
author:
- first_name: St.
  full_name: Baier, St.
  last_name: Baier
- first_name: D.
  full_name: Mazumder, D.
  last_name: Mazumder
- first_name: Marc
  full_name: Technau, Marc
  id: '106108'
  last_name: Technau
  orcid: 0000-0001-9650-2459
citation:
  ama: Baier St, Mazumder D, Technau M. On the distribution of αp modulo one in quadratic
    number fields. <i>Unif Distrib Theory</i>. 2021;16(2):1–48. doi:<a href="https://doi.org/10.2478/udt-2021-0006">10.2478/udt-2021-0006</a>
  apa: Baier, St., Mazumder, D., &#38; Technau, M. (2021). On the distribution of
    αp modulo one in quadratic number fields. <i>Unif. Distrib. Theory</i>, <i>16</i>(2),
    1–48. <a href="https://doi.org/10.2478/udt-2021-0006">https://doi.org/10.2478/udt-2021-0006</a>
  bibtex: '@article{Baier_Mazumder_Technau_2021, title={On the distribution of αp
    modulo one in quadratic number fields}, volume={16}, DOI={<a href="https://doi.org/10.2478/udt-2021-0006">10.2478/udt-2021-0006</a>},
    number={2}, journal={Unif. Distrib. Theory}, author={Baier, St. and Mazumder,
    D. and Technau, Marc}, year={2021}, pages={1–48} }'
  chicago: 'Baier, St., D. Mazumder, and Marc Technau. “On the Distribution of Αp
    modulo One in Quadratic Number Fields.” <i>Unif. Distrib. Theory</i> 16, no. 2
    (2021): 1–48. <a href="https://doi.org/10.2478/udt-2021-0006">https://doi.org/10.2478/udt-2021-0006</a>.'
  ieee: 'St. Baier, D. Mazumder, and M. Technau, “On the distribution of αp modulo
    one in quadratic number fields,” <i>Unif. Distrib. Theory</i>, vol. 16, no. 2,
    pp. 1–48, 2021, doi: <a href="https://doi.org/10.2478/udt-2021-0006">10.2478/udt-2021-0006</a>.'
  mla: Baier, St., et al. “On the Distribution of Αp modulo One in Quadratic Number
    Fields.” <i>Unif. Distrib. Theory</i>, vol. 16, no. 2, 2021, pp. 1–48, doi:<a
    href="https://doi.org/10.2478/udt-2021-0006">10.2478/udt-2021-0006</a>.
  short: St. Baier, D. Mazumder, M. Technau, Unif. Distrib. Theory 16 (2021) 1–48.
date_created: 2024-07-16T11:09:03Z
date_updated: 2024-07-24T07:23:43Z
department:
- _id: '102'
doi: 10.2478/udt-2021-0006
extern: '1'
intvolume: '        16'
issue: '2'
language:
- iso: eng
page: 1–48
publication: Unif. Distrib. Theory
status: public
title: On the distribution of αp modulo one in quadratic number fields
type: journal_article
user_id: '106108'
volume: 16
year: '2021'
...
---
_id: '55289'
author:
- first_name: Marc
  full_name: Technau, Marc
  id: '106108'
  last_name: Technau
  orcid: 0000-0001-9650-2459
- first_name: A.
  full_name: Zafeiropoulos, A.
  last_name: Zafeiropoulos
citation:
  ama: Technau M, Zafeiropoulos A. Metric results on summatory arithmetic functions
    on Beatty sets. <i>Acta Arith</i>. 2021;197(1):93–104. doi:<a href="https://doi.org/10.4064/aa200128-10-6">10.4064/aa200128-10-6</a>
  apa: Technau, M., &#38; Zafeiropoulos, A. (2021). Metric results on summatory arithmetic
    functions on Beatty sets. <i>Acta Arith.</i>, <i>197</i>(1), 93–104. <a href="https://doi.org/10.4064/aa200128-10-6">https://doi.org/10.4064/aa200128-10-6</a>
  bibtex: '@article{Technau_Zafeiropoulos_2021, title={Metric results on summatory
    arithmetic functions on Beatty sets}, volume={197}, DOI={<a href="https://doi.org/10.4064/aa200128-10-6">10.4064/aa200128-10-6</a>},
    number={1}, journal={Acta Arith.}, author={Technau, Marc and Zafeiropoulos, A.},
    year={2021}, pages={93–104} }'
  chicago: 'Technau, Marc, and A. Zafeiropoulos. “Metric Results on Summatory Arithmetic
    Functions on Beatty Sets.” <i>Acta Arith.</i> 197, no. 1 (2021): 93–104. <a href="https://doi.org/10.4064/aa200128-10-6">https://doi.org/10.4064/aa200128-10-6</a>.'
  ieee: 'M. Technau and A. Zafeiropoulos, “Metric results on summatory arithmetic
    functions on Beatty sets,” <i>Acta Arith.</i>, vol. 197, no. 1, pp. 93–104, 2021,
    doi: <a href="https://doi.org/10.4064/aa200128-10-6">10.4064/aa200128-10-6</a>.'
  mla: Technau, Marc, and A. Zafeiropoulos. “Metric Results on Summatory Arithmetic
    Functions on Beatty Sets.” <i>Acta Arith.</i>, vol. 197, no. 1, 2021, pp. 93–104,
    doi:<a href="https://doi.org/10.4064/aa200128-10-6">10.4064/aa200128-10-6</a>.
  short: M. Technau, A. Zafeiropoulos, Acta Arith. 197 (2021) 93–104.
date_created: 2024-07-16T11:09:03Z
date_updated: 2024-07-24T07:25:48Z
department:
- _id: '102'
doi: 10.4064/aa200128-10-6
extern: '1'
intvolume: '       197'
issue: '1'
language:
- iso: eng
page: 93–104
publication: Acta Arith.
status: public
title: Metric results on summatory arithmetic functions on Beatty sets
type: journal_article
user_id: '106108'
volume: 197
year: '2021'
...
---
_id: '34840'
abstract:
- lang: eng
  text: 'In this paper we obtain a complete list of imaginary n-quadratic fields with
    class groups of exponent 3 and 5 under ERH for every positive integer n where
    an n-quadratic field is a number field of degree 2ⁿ represented as the composite
    of n quadratic fields. '
author:
- first_name: Jürgen
  full_name: Klüners, Jürgen
  id: '21202'
  last_name: Klüners
- first_name: Toru
  full_name: Komatsu, Toru
  last_name: Komatsu
citation:
  ama: Klüners J, Komatsu T. Imaginary multiquadratic number fields with class group
    of exponent $3$ and $5$. <i>Mathematics of Computation</i>. 2021;90(329):1483-1497.
    doi:<a href="https://doi.org/10.1090/mcom/3609">10.1090/mcom/3609</a>
  apa: Klüners, J., &#38; Komatsu, T. (2021). Imaginary multiquadratic number fields
    with class group of exponent $3$ and $5$. <i>Mathematics of Computation</i>, <i>90</i>(329),
    1483–1497. <a href="https://doi.org/10.1090/mcom/3609">https://doi.org/10.1090/mcom/3609</a>
  bibtex: '@article{Klüners_Komatsu_2021, title={Imaginary multiquadratic number fields
    with class group of exponent $3$ and $5$}, volume={90}, DOI={<a href="https://doi.org/10.1090/mcom/3609">10.1090/mcom/3609</a>},
    number={329}, journal={Mathematics of Computation}, publisher={American Mathematical
    Society (AMS)}, author={Klüners, Jürgen and Komatsu, Toru}, year={2021}, pages={1483–1497}
    }'
  chicago: 'Klüners, Jürgen, and Toru Komatsu. “Imaginary Multiquadratic Number Fields
    with Class Group of Exponent $3$ and $5$.” <i>Mathematics of Computation</i> 90,
    no. 329 (2021): 1483–97. <a href="https://doi.org/10.1090/mcom/3609">https://doi.org/10.1090/mcom/3609</a>.'
  ieee: 'J. Klüners and T. Komatsu, “Imaginary multiquadratic number fields with class
    group of exponent $3$ and $5$,” <i>Mathematics of Computation</i>, vol. 90, no.
    329, pp. 1483–1497, 2021, doi: <a href="https://doi.org/10.1090/mcom/3609">10.1090/mcom/3609</a>.'
  mla: Klüners, Jürgen, and Toru Komatsu. “Imaginary Multiquadratic Number Fields
    with Class Group of Exponent $3$ and $5$.” <i>Mathematics of Computation</i>,
    vol. 90, no. 329, American Mathematical Society (AMS), 2021, pp. 1483–97, doi:<a
    href="https://doi.org/10.1090/mcom/3609">10.1090/mcom/3609</a>.
  short: J. Klüners, T. Komatsu, Mathematics of Computation 90 (2021) 1483–1497.
date_created: 2022-12-22T10:48:44Z
date_updated: 2023-03-06T08:57:45Z
department:
- _id: '102'
doi: 10.1090/mcom/3609
external_id:
  arxiv:
  - 2004.03308v2
intvolume: '        90'
issue: '329'
keyword:
- Applied Mathematics
- Computational Mathematics
- Algebra and Number Theory
language:
- iso: eng
page: 1483-1497
publication: Mathematics of Computation
publication_identifier:
  issn:
  - 0025-5718
  - 1088-6842
publication_status: published
publisher: American Mathematical Society (AMS)
status: public
title: Imaginary multiquadratic number fields with class group of exponent $3$ and
  $5$
type: journal_article
user_id: '93826'
volume: 90
year: '2021'
...
---
_id: '34912'
abstract:
- lang: eng
  text: 'Let E be an ordinary elliptic curve over a finite field and g be a positive
    integer. Under some technical assumptions, we give an algorithm to span the isomorphism
    classes of principally polarized abelian varieties in the isogeny class of E⁹
    . The varieties are first described as hermitian lattices over (not necessarily
    maximal) quadratic orders and then geometrically in terms of their algebraic theta
    null point. We also show how to algebraically compute Siegel modular forms of
    even weight given as polynomials in the theta constants by a careful choice of
    an affine lift of the theta null point. We then use these results to give an algebraic
    computation of Serre’s obstruction for principally polarized abelian threefolds
    isogenous to E³ and of the Igusa modular form in dimension 4. We illustrate our
    algorithms with examples of curves with many rational points over finite fields. '
author:
- first_name: Markus
  full_name: Kirschmer, Markus
  id: '82258'
  last_name: Kirschmer
- first_name: Fabien
  full_name: Narbonne, Fabien
  last_name: Narbonne
- first_name: Christophe
  full_name: Ritzenthaler, Christophe
  last_name: Ritzenthaler
- first_name: Damien
  full_name: Robert, Damien
  last_name: Robert
citation:
  ama: Kirschmer M, Narbonne F, Ritzenthaler C, Robert D. Spanning the isogeny class
    of a power of an elliptic curve. <i>Mathematics of Computation</i>. 2021;91(333):401-449.
    doi:<a href="https://doi.org/10.1090/mcom/3672">10.1090/mcom/3672</a>
  apa: Kirschmer, M., Narbonne, F., Ritzenthaler, C., &#38; Robert, D. (2021). Spanning
    the isogeny class of a power of an elliptic curve. <i>Mathematics of Computation</i>,
    <i>91</i>(333), 401–449. <a href="https://doi.org/10.1090/mcom/3672">https://doi.org/10.1090/mcom/3672</a>
  bibtex: '@article{Kirschmer_Narbonne_Ritzenthaler_Robert_2021, title={Spanning the
    isogeny class of a power of an elliptic curve}, volume={91}, DOI={<a href="https://doi.org/10.1090/mcom/3672">10.1090/mcom/3672</a>},
    number={333}, journal={Mathematics of Computation}, publisher={American Mathematical
    Society (AMS)}, author={Kirschmer, Markus and Narbonne, Fabien and Ritzenthaler,
    Christophe and Robert, Damien}, year={2021}, pages={401–449} }'
  chicago: 'Kirschmer, Markus, Fabien Narbonne, Christophe Ritzenthaler, and Damien
    Robert. “Spanning the Isogeny Class of a Power of an Elliptic Curve.” <i>Mathematics
    of Computation</i> 91, no. 333 (2021): 401–49. <a href="https://doi.org/10.1090/mcom/3672">https://doi.org/10.1090/mcom/3672</a>.'
  ieee: 'M. Kirschmer, F. Narbonne, C. Ritzenthaler, and D. Robert, “Spanning the
    isogeny class of a power of an elliptic curve,” <i>Mathematics of Computation</i>,
    vol. 91, no. 333, pp. 401–449, 2021, doi: <a href="https://doi.org/10.1090/mcom/3672">10.1090/mcom/3672</a>.'
  mla: Kirschmer, Markus, et al. “Spanning the Isogeny Class of a Power of an Elliptic
    Curve.” <i>Mathematics of Computation</i>, vol. 91, no. 333, American Mathematical
    Society (AMS), 2021, pp. 401–49, doi:<a href="https://doi.org/10.1090/mcom/3672">10.1090/mcom/3672</a>.
  short: M. Kirschmer, F. Narbonne, C. Ritzenthaler, D. Robert, Mathematics of Computation
    91 (2021) 401–449.
date_created: 2022-12-23T11:02:02Z
date_updated: 2023-04-04T07:52:43Z
department:
- _id: '102'
doi: 10.1090/mcom/3672
intvolume: '        91'
issue: '333'
keyword:
- Applied Mathematics
- Computational Mathematics
- Algebra and Number Theory
language:
- iso: eng
page: 401-449
publication: Mathematics of Computation
publication_identifier:
  issn:
  - 0025-5718
  - 1088-6842
publication_status: published
publisher: American Mathematical Society (AMS)
status: public
title: Spanning the isogeny class of a power of an elliptic curve
type: journal_article
user_id: '93826'
volume: 91
year: '2021'
...
---
_id: '55288'
author:
- first_name: St.
  full_name: Baier, St.
  last_name: Baier
- first_name: Marc
  full_name: Technau, Marc
  id: '106108'
  last_name: Technau
  orcid: 0000-0001-9650-2459
citation:
  ama: Baier St, Technau M. On the distribution of αp modulo one in imaginary quadratic
    number fields with class number one. <i>J Théor Nombres Bordx</i>. 2020;32(2):719–760.
    doi:<a href="https://doi.org/10.5802/jtnb.1141">10.5802/jtnb.1141</a>
  apa: Baier, St., &#38; Technau, M. (2020). On the distribution of αp modulo one
    in imaginary quadratic number fields with class number one. <i>J. Théor. Nombres
    Bordx.</i>, <i>32</i>(2), 719–760. <a href="https://doi.org/10.5802/jtnb.1141">https://doi.org/10.5802/jtnb.1141</a>
  bibtex: '@article{Baier_Technau_2020, title={On the distribution of αp modulo one
    in imaginary quadratic number fields with class number one}, volume={32}, DOI={<a
    href="https://doi.org/10.5802/jtnb.1141">10.5802/jtnb.1141</a>}, number={2}, journal={J.
    Théor. Nombres Bordx.}, author={Baier, St. and Technau, Marc}, year={2020}, pages={719–760}
    }'
  chicago: 'Baier, St., and Marc Technau. “On the Distribution of Αp modulo One in
    Imaginary Quadratic Number Fields with Class Number One.” <i>J. Théor. Nombres
    Bordx.</i> 32, no. 2 (2020): 719–760. <a href="https://doi.org/10.5802/jtnb.1141">https://doi.org/10.5802/jtnb.1141</a>.'
  ieee: 'St. Baier and M. Technau, “On the distribution of αp modulo one in imaginary
    quadratic number fields with class number one,” <i>J. Théor. Nombres Bordx.</i>,
    vol. 32, no. 2, pp. 719–760, 2020, doi: <a href="https://doi.org/10.5802/jtnb.1141">10.5802/jtnb.1141</a>.'
  mla: Baier, St., and Marc Technau. “On the Distribution of Αp modulo One in Imaginary
    Quadratic Number Fields with Class Number One.” <i>J. Théor. Nombres Bordx.</i>,
    vol. 32, no. 2, 2020, pp. 719–760, doi:<a href="https://doi.org/10.5802/jtnb.1141">10.5802/jtnb.1141</a>.
  short: St. Baier, M. Technau, J. Théor. Nombres Bordx. 32 (2020) 719–760.
date_created: 2024-07-16T11:09:02Z
date_updated: 2024-07-24T07:23:57Z
department:
- _id: '102'
doi: 10.5802/jtnb.1141
intvolume: '        32'
issue: '2'
language:
- iso: eng
page: 719–760
publication: J. Théor. Nombres Bordx.
status: public
title: On the distribution of αp modulo one in imaginary quadratic number fields with
  class number one
type: journal_article
user_id: '106108'
volume: 32
year: '2020'
...
---
_id: '55286'
author:
- first_name: Marc
  full_name: Technau, Marc
  id: '106108'
  last_name: Technau
  orcid: 0000-0001-9650-2459
citation:
  ama: Technau M. Modular hyperbolas and Beatty sequences. <i>J Number Theory</i>.
    2020;208:148–167. doi:<a href="https://doi.org/10.1016/j.jnt.2019.07.022">10.1016/j.jnt.2019.07.022</a>
  apa: Technau, M. (2020). Modular hyperbolas and Beatty sequences. <i>J. Number Theory</i>,
    <i>208</i>, 148–167. <a href="https://doi.org/10.1016/j.jnt.2019.07.022">https://doi.org/10.1016/j.jnt.2019.07.022</a>
  bibtex: '@article{Technau_2020, title={Modular hyperbolas and Beatty sequences},
    volume={208}, DOI={<a href="https://doi.org/10.1016/j.jnt.2019.07.022">10.1016/j.jnt.2019.07.022</a>},
    journal={J. Number Theory}, author={Technau, Marc}, year={2020}, pages={148–167}
    }'
  chicago: 'Technau, Marc. “Modular Hyperbolas and Beatty Sequences.” <i>J. Number
    Theory</i> 208 (2020): 148–167. <a href="https://doi.org/10.1016/j.jnt.2019.07.022">https://doi.org/10.1016/j.jnt.2019.07.022</a>.'
  ieee: 'M. Technau, “Modular hyperbolas and Beatty sequences,” <i>J. Number Theory</i>,
    vol. 208, pp. 148–167, 2020, doi: <a href="https://doi.org/10.1016/j.jnt.2019.07.022">10.1016/j.jnt.2019.07.022</a>.'
  mla: Technau, Marc. “Modular Hyperbolas and Beatty Sequences.” <i>J. Number Theory</i>,
    vol. 208, 2020, pp. 148–167, doi:<a href="https://doi.org/10.1016/j.jnt.2019.07.022">10.1016/j.jnt.2019.07.022</a>.
  short: M. Technau, J. Number Theory 208 (2020) 148–167.
date_created: 2024-07-16T11:09:02Z
date_updated: 2024-07-24T07:24:11Z
department:
- _id: '102'
doi: 10.1016/j.jnt.2019.07.022
extern: '1'
intvolume: '       208'
language:
- iso: eng
page: 148–167
publication: J. Number Theory
status: public
title: Modular hyperbolas and Beatty sequences
type: journal_article
user_id: '106108'
volume: 208
year: '2020'
...
---
_id: '55287'
author:
- first_name: I. E.
  full_name: Shparlinski, I. E.
  last_name: Shparlinski
- first_name: Marc
  full_name: Technau, Marc
  id: '106108'
  last_name: Technau
  orcid: 0000-0001-9650-2459
citation:
  ama: Shparlinski IE, Technau M. Kloosterman sums with twice-differentiable functions.
    <i>Funct Approximatio, Comment Math</i>. 2020;63(1):113–124. doi:<a href="https://doi.org/10.7169/facm/1845">10.7169/facm/1845</a>
  apa: Shparlinski, I. E., &#38; Technau, M. (2020). Kloosterman sums with twice-differentiable
    functions. <i>Funct. Approximatio, Comment. Math.</i>, <i>63</i>(1), 113–124.
    <a href="https://doi.org/10.7169/facm/1845">https://doi.org/10.7169/facm/1845</a>
  bibtex: '@article{Shparlinski_Technau_2020, title={Kloosterman sums with twice-differentiable
    functions}, volume={63}, DOI={<a href="https://doi.org/10.7169/facm/1845">10.7169/facm/1845</a>},
    number={1}, journal={Funct. Approximatio, Comment. Math.}, author={Shparlinski,
    I. E. and Technau, Marc}, year={2020}, pages={113–124} }'
  chicago: 'Shparlinski, I. E., and Marc Technau. “Kloosterman Sums with Twice-Differentiable
    Functions.” <i>Funct. Approximatio, Comment. Math.</i> 63, no. 1 (2020): 113–124.
    <a href="https://doi.org/10.7169/facm/1845">https://doi.org/10.7169/facm/1845</a>.'
  ieee: 'I. E. Shparlinski and M. Technau, “Kloosterman sums with twice-differentiable
    functions,” <i>Funct. Approximatio, Comment. Math.</i>, vol. 63, no. 1, pp. 113–124,
    2020, doi: <a href="https://doi.org/10.7169/facm/1845">10.7169/facm/1845</a>.'
  mla: Shparlinski, I. E., and Marc Technau. “Kloosterman Sums with Twice-Differentiable
    Functions.” <i>Funct. Approximatio, Comment. Math.</i>, vol. 63, no. 1, 2020,
    pp. 113–124, doi:<a href="https://doi.org/10.7169/facm/1845">10.7169/facm/1845</a>.
  short: I.E. Shparlinski, M. Technau, Funct. Approximatio, Comment. Math. 63 (2020)
    113–124.
date_created: 2024-07-16T11:09:02Z
date_updated: 2024-07-24T07:25:54Z
department:
- _id: '102'
doi: 10.7169/facm/1845
extern: '1'
intvolume: '        63'
issue: '1'
language:
- iso: eng
page: 113–124
publication: Funct. Approximatio, Comment. Math.
status: public
title: Kloosterman sums with twice-differentiable functions
type: journal_article
user_id: '106108'
volume: 63
year: '2020'
...
---
_id: '55283'
author:
- first_name: D.
  full_name: Barth, D.
  last_name: Barth
- first_name: M.
  full_name: Beck, M.
  last_name: Beck
- first_name: T.
  full_name: Dose, T.
  last_name: Dose
- first_name: Ch.
  full_name: Glaßer, Ch.
  last_name: Glaßer
- first_name: L.
  full_name: Michler, L.
  last_name: Michler
- first_name: Marc
  full_name: Technau, Marc
  id: '106108'
  last_name: Technau
  orcid: 0000-0001-9650-2459
citation:
  ama: Barth D, Beck M, Dose T, Glaßer Ch, Michler L, Technau M. Emptiness problems
    for integer circuits. <i>Theoretical Computer Science</i>. 2020;824-825:11–35.
    doi:<a href="https://doi.org/10.1016/j.tcs.2020.03.023">10.1016/j.tcs.2020.03.023</a>
  apa: Barth, D., Beck, M., Dose, T., Glaßer, Ch., Michler, L., &#38; Technau, M.
    (2020). Emptiness problems for integer circuits. <i>Theoretical Computer Science</i>,
    <i>824–825</i>, 11–35. <a href="https://doi.org/10.1016/j.tcs.2020.03.023">https://doi.org/10.1016/j.tcs.2020.03.023</a>
  bibtex: '@article{Barth_Beck_Dose_Glaßer_Michler_Technau_2020, title={Emptiness
    problems for integer circuits}, volume={824–825}, DOI={<a href="https://doi.org/10.1016/j.tcs.2020.03.023">10.1016/j.tcs.2020.03.023</a>},
    journal={Theoretical Computer Science}, author={Barth, D. and Beck, M. and Dose,
    T. and Glaßer, Ch. and Michler, L. and Technau, Marc}, year={2020}, pages={11–35}
    }'
  chicago: 'Barth, D., M. Beck, T. Dose, Ch. Glaßer, L. Michler, and Marc Technau.
    “Emptiness Problems for Integer Circuits.” <i>Theoretical Computer Science</i>
    824–825 (2020): 11–35. <a href="https://doi.org/10.1016/j.tcs.2020.03.023">https://doi.org/10.1016/j.tcs.2020.03.023</a>.'
  ieee: 'D. Barth, M. Beck, T. Dose, Ch. Glaßer, L. Michler, and M. Technau, “Emptiness
    problems for integer circuits,” <i>Theoretical Computer Science</i>, vol. 824–825,
    pp. 11–35, 2020, doi: <a href="https://doi.org/10.1016/j.tcs.2020.03.023">10.1016/j.tcs.2020.03.023</a>.'
  mla: Barth, D., et al. “Emptiness Problems for Integer Circuits.” <i>Theoretical
    Computer Science</i>, vol. 824–825, 2020, pp. 11–35, doi:<a href="https://doi.org/10.1016/j.tcs.2020.03.023">10.1016/j.tcs.2020.03.023</a>.
  short: D. Barth, M. Beck, T. Dose, Ch. Glaßer, L. Michler, M. Technau, Theoretical
    Computer Science 824–825 (2020) 11–35.
date_created: 2024-07-16T11:09:02Z
date_updated: 2024-07-24T07:25:29Z
department:
- _id: '102'
doi: 10.1016/j.tcs.2020.03.023
extern: '1'
language:
- iso: eng
page: 11–35
publication: Theoretical Computer Science
status: public
title: Emptiness problems for integer circuits
type: journal_article
user_id: '106108'
volume: 824-825
year: '2020'
...
---
_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: '34841'
abstract:
- lang: eng
  text: "We give an exact formula for the number of G-extensions of local function
    fields Fq((t)) for finite abelian groups G up to a conductor bound. As an application
    we give a lower bound for the corresponding counting problem by discriminant.\r\n"
author:
- first_name: Jürgen
  full_name: Klüners, Jürgen
  id: '21202'
  last_name: Klüners
- first_name: Raphael
  full_name: Müller, Raphael
  last_name: Müller
citation:
  ama: Klüners J, Müller R. The conductor density of local function fields with abelian
    Galois group. <i>Journal of Number Theory</i>. 2020;212:311-322. doi:<a href="https://doi.org/10.1016/j.jnt.2019.11.007">10.1016/j.jnt.2019.11.007</a>
  apa: Klüners, J., &#38; Müller, R. (2020). The conductor density of local function
    fields with abelian Galois group. <i>Journal of Number Theory</i>, <i>212</i>,
    311–322. <a href="https://doi.org/10.1016/j.jnt.2019.11.007">https://doi.org/10.1016/j.jnt.2019.11.007</a>
  bibtex: '@article{Klüners_Müller_2020, title={The conductor density of local function
    fields with abelian Galois group}, volume={212}, DOI={<a href="https://doi.org/10.1016/j.jnt.2019.11.007">10.1016/j.jnt.2019.11.007</a>},
    journal={Journal of Number Theory}, publisher={Elsevier BV}, author={Klüners,
    Jürgen and Müller, Raphael}, year={2020}, pages={311–322} }'
  chicago: 'Klüners, Jürgen, and Raphael Müller. “The Conductor Density of Local Function
    Fields with Abelian Galois Group.” <i>Journal of Number Theory</i> 212 (2020):
    311–22. <a href="https://doi.org/10.1016/j.jnt.2019.11.007">https://doi.org/10.1016/j.jnt.2019.11.007</a>.'
  ieee: 'J. Klüners and R. Müller, “The conductor density of local function fields
    with abelian Galois group,” <i>Journal of Number Theory</i>, vol. 212, pp. 311–322,
    2020, doi: <a href="https://doi.org/10.1016/j.jnt.2019.11.007">10.1016/j.jnt.2019.11.007</a>.'
  mla: Klüners, Jürgen, and Raphael Müller. “The Conductor Density of Local Function
    Fields with Abelian Galois Group.” <i>Journal of Number Theory</i>, vol. 212,
    Elsevier BV, 2020, pp. 311–22, doi:<a href="https://doi.org/10.1016/j.jnt.2019.11.007">10.1016/j.jnt.2019.11.007</a>.
  short: J. Klüners, R. Müller, Journal of Number Theory 212 (2020) 311–322.
date_created: 2022-12-22T10:50:03Z
date_updated: 2025-06-13T08:18:30Z
department:
- _id: '102'
doi: 10.1016/j.jnt.2019.11.007
external_id:
  arxiv:
  - '1904.02573 '
intvolume: '       212'
keyword:
- Algebra and Number Theory
language:
- iso: eng
page: 311-322
publication: Journal of Number Theory
publication_identifier:
  issn:
  - 0022-314X
publication_status: published
publisher: Elsevier BV
status: public
title: The conductor density of local function fields with abelian Galois group
type: journal_article
user_id: '82981'
volume: 212
year: '2020'
...
---
_id: '34917'
abstract:
- lang: eng
  text: We relate proper isometry classes of maximal lattices in a totally definite
    quaternary quadratic space (V,q) with trivial discriminant to certain equivalence
    classes of ideals in the quaternion algebra representing the Clifford invariant
    of (V,q). This yields a good algorithm to enumerate a system of representatives
    of proper isometry classes of lattices in genera of maximal lattices in (V,q).
author:
- first_name: Markus
  full_name: Kirschmer, Markus
  id: '82258'
  last_name: Kirschmer
- first_name: Gabriele
  full_name: Nebe, Gabriele
  last_name: Nebe
citation:
  ama: Kirschmer M, Nebe G. Quaternary quadratic lattices over number fields. <i>International
    Journal of Number Theory</i>. 2019;15(02):309-325. doi:<a href="https://doi.org/10.1142/s1793042119500131">10.1142/s1793042119500131</a>
  apa: Kirschmer, M., &#38; Nebe, G. (2019). Quaternary quadratic lattices over number
    fields. <i>International Journal of Number Theory</i>, <i>15</i>(02), 309–325.
    <a href="https://doi.org/10.1142/s1793042119500131">https://doi.org/10.1142/s1793042119500131</a>
  bibtex: '@article{Kirschmer_Nebe_2019, title={Quaternary quadratic lattices over
    number fields}, volume={15}, DOI={<a href="https://doi.org/10.1142/s1793042119500131">10.1142/s1793042119500131</a>},
    number={02}, journal={International Journal of Number Theory}, publisher={World
    Scientific Pub Co Pte Lt}, author={Kirschmer, Markus and Nebe, Gabriele}, year={2019},
    pages={309–325} }'
  chicago: 'Kirschmer, Markus, and Gabriele Nebe. “Quaternary Quadratic Lattices over
    Number Fields.” <i>International Journal of Number Theory</i> 15, no. 02 (2019):
    309–25. <a href="https://doi.org/10.1142/s1793042119500131">https://doi.org/10.1142/s1793042119500131</a>.'
  ieee: 'M. Kirschmer and G. Nebe, “Quaternary quadratic lattices over number fields,”
    <i>International Journal of Number Theory</i>, vol. 15, no. 02, pp. 309–325, 2019,
    doi: <a href="https://doi.org/10.1142/s1793042119500131">10.1142/s1793042119500131</a>.'
  mla: Kirschmer, Markus, and Gabriele Nebe. “Quaternary Quadratic Lattices over Number
    Fields.” <i>International Journal of Number Theory</i>, vol. 15, no. 02, World
    Scientific Pub Co Pte Lt, 2019, pp. 309–25, doi:<a href="https://doi.org/10.1142/s1793042119500131">10.1142/s1793042119500131</a>.
  short: M. Kirschmer, G. Nebe, International Journal of Number Theory 15 (2019) 309–325.
date_created: 2022-12-23T11:05:09Z
date_updated: 2023-12-06T10:05:59Z
department:
- _id: '102'
doi: 10.1142/s1793042119500131
intvolume: '        15'
issue: '02'
keyword:
- Algebra and Number Theory
language:
- iso: eng
page: 309-325
publication: International Journal of Number Theory
publication_identifier:
  issn:
  - 1793-0421
  - 1793-7310
publication_status: published
publisher: World Scientific Pub Co Pte Lt
status: public
title: Quaternary quadratic lattices over number fields
type: journal_article
user_id: '82258'
volume: 15
year: '2019'
...