---
_id: '34893'
abstract:
- lang: eng
  text: Let K be a global field and O be an order of K. We develop algorithms for
    the computation of the unit group of residue class rings for ideals O in . As
    an application we show how to compute the unit group and the Picard group of O
    provided that we are able to compute the unit group and class group of the maximal
    order O of K.
author:
- first_name: Jürgen
  full_name: Klüners, Jürgen
  id: '21202'
  last_name: Klüners
- first_name: Sebastian
  full_name: Pauli, Sebastian
  last_name: Pauli
citation:
  ama: Klüners J, Pauli S. Computing residue class rings and Picard groups of orders.
    <i>Journal of Algebra</i>. 2005;292(1):47-64. doi:<a href="https://doi.org/10.1016/j.jalgebra.2005.04.013">10.1016/j.jalgebra.2005.04.013</a>
  apa: Klüners, J., &#38; Pauli, S. (2005). Computing residue class rings and Picard
    groups of orders. <i>Journal of Algebra</i>, <i>292</i>(1), 47–64. <a href="https://doi.org/10.1016/j.jalgebra.2005.04.013">https://doi.org/10.1016/j.jalgebra.2005.04.013</a>
  bibtex: '@article{Klüners_Pauli_2005, title={Computing residue class rings and Picard
    groups of orders}, volume={292}, DOI={<a href="https://doi.org/10.1016/j.jalgebra.2005.04.013">10.1016/j.jalgebra.2005.04.013</a>},
    number={1}, journal={Journal of Algebra}, publisher={Elsevier BV}, author={Klüners,
    Jürgen and Pauli, Sebastian}, year={2005}, pages={47–64} }'
  chicago: 'Klüners, Jürgen, and Sebastian Pauli. “Computing Residue Class Rings and
    Picard Groups of Orders.” <i>Journal of Algebra</i> 292, no. 1 (2005): 47–64.
    <a href="https://doi.org/10.1016/j.jalgebra.2005.04.013">https://doi.org/10.1016/j.jalgebra.2005.04.013</a>.'
  ieee: 'J. Klüners and S. Pauli, “Computing residue class rings and Picard groups
    of orders,” <i>Journal of Algebra</i>, vol. 292, no. 1, pp. 47–64, 2005, doi:
    <a href="https://doi.org/10.1016/j.jalgebra.2005.04.013">10.1016/j.jalgebra.2005.04.013</a>.'
  mla: Klüners, Jürgen, and Sebastian Pauli. “Computing Residue Class Rings and Picard
    Groups of Orders.” <i>Journal of Algebra</i>, vol. 292, no. 1, Elsevier BV, 2005,
    pp. 47–64, doi:<a href="https://doi.org/10.1016/j.jalgebra.2005.04.013">10.1016/j.jalgebra.2005.04.013</a>.
  short: J. Klüners, S. Pauli, Journal of Algebra 292 (2005) 47–64.
date_created: 2022-12-23T09:41:06Z
date_updated: 2023-03-06T09:55:09Z
department:
- _id: '102'
doi: 10.1016/j.jalgebra.2005.04.013
intvolume: '       292'
issue: '1'
keyword:
- Algebra and Number Theory
language:
- iso: eng
page: 47-64
publication: Journal of Algebra
publication_identifier:
  issn:
  - 0021-8693
publication_status: published
publisher: Elsevier BV
status: public
title: Computing residue class rings and Picard groups of orders
type: journal_article
user_id: '93826'
volume: 292
year: '2005'
...
---
_id: '42807'
author:
- first_name: Jürgen
  full_name: Klüners, Jürgen
  id: '21202'
  last_name: Klüners
citation:
  ama: Klüners J. <i>Über die Asymptotik von Zahlkörpern mit vorgegebener Galoisgruppe
    (Habilitation)</i>. Shaker Verlag; 2005.
  apa: Klüners, J. (2005). <i>Über die Asymptotik von Zahlkörpern mit vorgegebener
    Galoisgruppe (Habilitation)</i>. Shaker Verlag.
  bibtex: '@book{Klüners_2005, place={Universiät Kassel}, title={Über die Asymptotik
    von Zahlkörpern mit vorgegebener Galoisgruppe (Habilitation)}, publisher={Shaker
    Verlag}, author={Klüners, Jürgen}, year={2005} }'
  chicago: 'Klüners, Jürgen. <i>Über die Asymptotik von Zahlkörpern mit vorgegebener
    Galoisgruppe (Habilitation)</i>. Universiät Kassel: Shaker Verlag, 2005.'
  ieee: 'J. Klüners, <i>Über die Asymptotik von Zahlkörpern mit vorgegebener Galoisgruppe
    (Habilitation)</i>. Universiät Kassel: Shaker Verlag, 2005.'
  mla: Klüners, Jürgen. <i>Über die Asymptotik von Zahlkörpern mit vorgegebener Galoisgruppe
    (Habilitation)</i>. Shaker Verlag, 2005.
  short: J. Klüners, Über die Asymptotik von Zahlkörpern mit vorgegebener Galoisgruppe
    (Habilitation), Shaker Verlag, Universiät Kassel, 2005.
date_created: 2023-03-07T09:05:29Z
date_updated: 2023-04-11T08:13:38Z
department:
- _id: '102'
extern: '1'
language:
- iso: ger
page: '114'
place: Universiät Kassel
publication_identifier:
  isbn:
  - 978-3-8322-4003-5
publisher: Shaker Verlag
status: public
title: Über die Asymptotik von Zahlkörpern mit vorgegebener Galoisgruppe (Habilitation)
type: misc
user_id: '93826'
year: '2005'
...
---
_id: '43455'
author:
- first_name: Markus
  full_name: Kirschmer, Markus
  id: '82258'
  last_name: Kirschmer
citation:
  ama: Kirschmer M. <i>Konstruktive Idealtheorie in Quaternionenalgebren (Diplomarbeit)</i>.;
    2005.
  apa: Kirschmer, M. (2005). <i>Konstruktive Idealtheorie in Quaternionenalgebren
    (Diplomarbeit)</i>.
  bibtex: '@book{Kirschmer_2005, place={Universität Ulm}, title={Konstruktive Idealtheorie
    in Quaternionenalgebren (Diplomarbeit)}, author={Kirschmer, Markus}, year={2005}
    }'
  chicago: Kirschmer, Markus. <i>Konstruktive Idealtheorie in Quaternionenalgebren
    (Diplomarbeit)</i>. Universität Ulm, 2005.
  ieee: M. Kirschmer, <i>Konstruktive Idealtheorie in Quaternionenalgebren (Diplomarbeit)</i>.
    Universität Ulm, 2005.
  mla: Kirschmer, Markus. <i>Konstruktive Idealtheorie in Quaternionenalgebren (Diplomarbeit)</i>.
    2005.
  short: M. Kirschmer, Konstruktive Idealtheorie in Quaternionenalgebren (Diplomarbeit),
    Universität Ulm, 2005.
date_created: 2023-04-11T08:09:29Z
date_updated: 2023-04-11T08:11:24Z
department:
- _id: '102'
extern: '1'
language:
- iso: eng
page: '147'
place: Universität Ulm
status: public
title: Konstruktive Idealtheorie in Quaternionenalgebren (Diplomarbeit)
type: mastersthesis
user_id: '93826'
year: '2005'
...
---
_id: '34896'
abstract:
- lang: eng
  text: We apply class field theory to the computation of the minimal discriminants
    for certain solvable groups. In particular, we apply our techniques to small Frobenius
    groups and all imprimitive degree 8 groups such that the corresponding fields
    have only a degree 2 and no degree 4 subfield.
author:
- first_name: Claus
  full_name: Fieker, Claus
  last_name: Fieker
- first_name: Jürgen
  full_name: Klüners, Jürgen
  id: '21202'
  last_name: Klüners
citation:
  ama: Fieker C, Klüners J. Minimal discriminants for fields with small Frobenius
    groups as Galois groups. <i>Journal of Number Theory</i>. 2003;99(2):318-337.
    doi:<a href="https://doi.org/10.1016/s0022-314x(02)00071-9">10.1016/s0022-314x(02)00071-9</a>
  apa: Fieker, C., &#38; Klüners, J. (2003). Minimal discriminants for fields with
    small Frobenius groups as Galois groups. <i>Journal of Number Theory</i>, <i>99</i>(2),
    318–337. <a href="https://doi.org/10.1016/s0022-314x(02)00071-9">https://doi.org/10.1016/s0022-314x(02)00071-9</a>
  bibtex: '@article{Fieker_Klüners_2003, title={Minimal discriminants for fields with
    small Frobenius groups as Galois groups}, volume={99}, DOI={<a href="https://doi.org/10.1016/s0022-314x(02)00071-9">10.1016/s0022-314x(02)00071-9</a>},
    number={2}, journal={Journal of Number Theory}, publisher={Elsevier BV}, author={Fieker,
    Claus and Klüners, Jürgen}, year={2003}, pages={318–337} }'
  chicago: 'Fieker, Claus, and Jürgen Klüners. “Minimal Discriminants for Fields with
    Small Frobenius Groups as Galois Groups.” <i>Journal of Number Theory</i> 99,
    no. 2 (2003): 318–37. <a href="https://doi.org/10.1016/s0022-314x(02)00071-9">https://doi.org/10.1016/s0022-314x(02)00071-9</a>.'
  ieee: 'C. Fieker and J. Klüners, “Minimal discriminants for fields with small Frobenius
    groups as Galois groups,” <i>Journal of Number Theory</i>, vol. 99, no. 2, pp.
    318–337, 2003, doi: <a href="https://doi.org/10.1016/s0022-314x(02)00071-9">10.1016/s0022-314x(02)00071-9</a>.'
  mla: Fieker, Claus, and Jürgen Klüners. “Minimal Discriminants for Fields with Small
    Frobenius Groups as Galois Groups.” <i>Journal of Number Theory</i>, vol. 99,
    no. 2, Elsevier BV, 2003, pp. 318–37, doi:<a href="https://doi.org/10.1016/s0022-314x(02)00071-9">10.1016/s0022-314x(02)00071-9</a>.
  short: C. Fieker, J. Klüners, Journal of Number Theory 99 (2003) 318–337.
date_created: 2022-12-23T09:53:23Z
date_updated: 2023-03-06T09:19:16Z
department:
- _id: '102'
doi: 10.1016/s0022-314x(02)00071-9
intvolume: '        99'
issue: '2'
keyword:
- Algebra and Number Theory
language:
- iso: eng
page: 318-337
publication: Journal of Number Theory
publication_identifier:
  issn:
  - 0022-314X
publication_status: published
publisher: Elsevier BV
status: public
title: Minimal discriminants for fields with small Frobenius groups as Galois groups
type: journal_article
user_id: '93826'
volume: 99
year: '2003'
...
---
_id: '35954'
abstract:
- lang: eng
  text: 'Let {\ASIE K}\,/{\small \ℚ}({\ASIE t \!}) be a finite extension. We describe
    algorithms for computing subfields and automorphisms of {\ASIE K}\,/{\small \ℚ}({\ASIE
    t }\!). As an application we give an algorithm for finding decompositions of rational
    functions in {\small \ℚ(α)}. We also present an algorithm which decides if an
    extension {\ASIE L}\,/{\small \ℚ}({\ASIE t \!}) is a subfield of {\ASIE K}. In
    case [{\ASIE K : \;}{\small\ℚ}({\ASIE t \!})] = [{\ASIE L : \;}{\small \ℚ}({\ASIE
    t \!})] we obtain a {\small \ℚ}({\ASIE t \!})-isomorphism test. Furthermore, we
    describe an algorithm which computes subfields of the normal closure of {\ASIE
    K}\,/{\small \ℚ}({\ASIE t \!}).'
author:
- first_name: Jürgen
  full_name: Klüners, Jürgen
  id: '21202'
  last_name: Klüners
citation:
  ama: Klüners J. Algorithms for function fields. <i>Experiment Math </i>. 2002;11(2):171-181.
  apa: Klüners, J. (2002). Algorithms for function fields. <i>Experiment. Math. </i>,
    <i>11</i>(2), 171–181.
  bibtex: '@article{Klüners_2002, title={Algorithms for function fields}, volume={11},
    number={2}, journal={Experiment. Math. }, publisher={Elsevier BV}, author={Klüners,
    Jürgen}, year={2002}, pages={171–181} }'
  chicago: 'Klüners, Jürgen. “Algorithms for Function Fields.” <i>Experiment. Math.
    </i> 11, no. 2 (2002): 171–81.'
  ieee: J. Klüners, “Algorithms for function fields,” <i>Experiment. Math. </i>, vol.
    11, no. 2, pp. 171–181, 2002.
  mla: Klüners, Jürgen. “Algorithms for Function Fields.” <i>Experiment. Math. </i>,
    vol. 11, no. 2, Elsevier BV, 2002, pp. 171–81.
  short: J. Klüners, Experiment. Math.  11 (2002) 171–181.
date_created: 2023-01-11T09:45:40Z
date_updated: 2023-03-06T10:26:58Z
department:
- _id: '102'
intvolume: '        11'
issue: '2'
keyword:
- algorithms
- decompositions
- Galois groups
- subfields
language:
- iso: eng
page: 171-181
publication: 'Experiment. Math. '
publication_status: published
publisher: Elsevier BV
related_material:
  link:
  - relation: confirmation
    url: https://projecteuclid.org/journals/experimental-mathematics/volume-11/issue-2/Algorithms-for-function-fields/em/1062621213.full
status: public
title: Algorithms for function fields
type: journal_article
user_id: '93826'
volume: 11
year: '2002'
...
---
_id: '34897'
abstract:
- lang: eng
  text: This paper announces the creation of a database for number fields. It describes
    the contents and the methods of access, indicates the origin of the polynomials,
    and formulates the aims of this collection of fields.
author:
- first_name: Jürgen
  full_name: Klüners, Jürgen
  id: '21202'
  last_name: Klüners
- first_name: Gunter
  full_name: Malle, Gunter
  last_name: Malle
citation:
  ama: Klüners J, Malle G. A Database for Field Extensions of the Rationals. <i>LMS
    Journal of Computation and Mathematics</i>. 2001;4:182-196. doi:<a href="https://doi.org/10.1112/s1461157000000851">10.1112/s1461157000000851</a>
  apa: Klüners, J., &#38; Malle, G. (2001). A Database for Field Extensions of the
    Rationals. <i>LMS Journal of Computation and Mathematics</i>, <i>4</i>, 182–196.
    <a href="https://doi.org/10.1112/s1461157000000851">https://doi.org/10.1112/s1461157000000851</a>
  bibtex: '@article{Klüners_Malle_2001, title={A Database for Field Extensions of
    the Rationals}, volume={4}, DOI={<a href="https://doi.org/10.1112/s1461157000000851">10.1112/s1461157000000851</a>},
    journal={LMS Journal of Computation and Mathematics}, publisher={Wiley}, author={Klüners,
    Jürgen and Malle, Gunter}, year={2001}, pages={182–196} }'
  chicago: 'Klüners, Jürgen, and Gunter Malle. “A Database for Field Extensions of
    the Rationals.” <i>LMS Journal of Computation and Mathematics</i> 4 (2001): 182–96.
    <a href="https://doi.org/10.1112/s1461157000000851">https://doi.org/10.1112/s1461157000000851</a>.'
  ieee: 'J. Klüners and G. Malle, “A Database for Field Extensions of the Rationals,”
    <i>LMS Journal of Computation and Mathematics</i>, vol. 4, pp. 182–196, 2001,
    doi: <a href="https://doi.org/10.1112/s1461157000000851">10.1112/s1461157000000851</a>.'
  mla: Klüners, Jürgen, and Gunter Malle. “A Database for Field Extensions of the
    Rationals.” <i>LMS Journal of Computation and Mathematics</i>, vol. 4, Wiley,
    2001, pp. 182–96, doi:<a href="https://doi.org/10.1112/s1461157000000851">10.1112/s1461157000000851</a>.
  short: J. Klüners, G. Malle, LMS Journal of Computation and Mathematics 4 (2001)
    182–196.
date_created: 2022-12-23T09:56:22Z
date_updated: 2023-03-02T09:53:08Z
department:
- _id: '102'
doi: 10.1112/s1461157000000851
external_id:
  arxiv:
  - math/0102232
intvolume: '         4'
keyword:
- Computational Theory and Mathematics
- General Mathematics
language:
- iso: eng
page: 182-196
publication: LMS Journal of Computation and Mathematics
publication_identifier:
  issn:
  - 1461-1570
publication_status: published
publisher: Wiley
status: public
title: A Database for Field Extensions of the Rationals
type: journal_article
user_id: '93826'
volume: 4
year: '2001'
...
---
_id: '34900'
abstract:
- lang: eng
  text: We describe methods for the computation of Galois groups of univariate polynomials
    over the rationals which we have implemented up to degree 15. These methods are
    based on Stauduhar’s algorithm. All computations are done in unramified p -adic
    extensions. For imprimitive groups we give an improvement using subfields. In
    the primitive case we use known subgroups of the Galois group together with a
    combination of Stauduhar’s method and the absolute resolvent method.
author:
- first_name: Katharina
  full_name: Geissler, Katharina
  last_name: Geissler
- first_name: Jürgen
  full_name: Klüners, Jürgen
  id: '21202'
  last_name: Klüners
citation:
  ama: Geissler K, Klüners J. Galois Group Computation for Rational Polynomials. <i>Journal
    of Symbolic Computation</i>. 2000;30(6):653-674. doi:<a href="https://doi.org/10.1006/jsco.2000.0377">10.1006/jsco.2000.0377</a>
  apa: Geissler, K., &#38; Klüners, J. (2000). Galois Group Computation for Rational
    Polynomials. <i>Journal of Symbolic Computation</i>, <i>30</i>(6), 653–674. <a
    href="https://doi.org/10.1006/jsco.2000.0377">https://doi.org/10.1006/jsco.2000.0377</a>
  bibtex: '@article{Geissler_Klüners_2000, title={Galois Group Computation for Rational
    Polynomials}, volume={30}, DOI={<a href="https://doi.org/10.1006/jsco.2000.0377">10.1006/jsco.2000.0377</a>},
    number={6}, journal={Journal of Symbolic Computation}, publisher={Elsevier BV},
    author={Geissler, Katharina and Klüners, Jürgen}, year={2000}, pages={653–674}
    }'
  chicago: 'Geissler, Katharina, and Jürgen Klüners. “Galois Group Computation for
    Rational Polynomials.” <i>Journal of Symbolic Computation</i> 30, no. 6 (2000):
    653–74. <a href="https://doi.org/10.1006/jsco.2000.0377">https://doi.org/10.1006/jsco.2000.0377</a>.'
  ieee: 'K. Geissler and J. Klüners, “Galois Group Computation for Rational Polynomials,”
    <i>Journal of Symbolic Computation</i>, vol. 30, no. 6, pp. 653–674, 2000, doi:
    <a href="https://doi.org/10.1006/jsco.2000.0377">10.1006/jsco.2000.0377</a>.'
  mla: Geissler, Katharina, and Jürgen Klüners. “Galois Group Computation for Rational
    Polynomials.” <i>Journal of Symbolic Computation</i>, vol. 30, no. 6, Elsevier
    BV, 2000, pp. 653–74, doi:<a href="https://doi.org/10.1006/jsco.2000.0377">10.1006/jsco.2000.0377</a>.
  short: K. Geissler, J. Klüners, Journal of Symbolic Computation 30 (2000) 653–674.
date_created: 2022-12-23T09:58:16Z
date_updated: 2023-03-06T09:58:06Z
department:
- _id: '102'
doi: 10.1006/jsco.2000.0377
intvolume: '        30'
issue: '6'
keyword:
- Computational Mathematics
- Algebra and Number Theory
language:
- iso: eng
page: 653-674
publication: Journal of Symbolic Computation
publication_identifier:
  issn:
  - 0747-7171
publication_status: published
publisher: Elsevier BV
status: public
title: Galois Group Computation for Rational Polynomials
type: journal_article
user_id: '93826'
volume: 30
year: '2000'
...
---
_id: '34901'
abstract:
- lang: eng
  text: Let L = K(α) be an Abelian extension of degree n of a number field K, given
    by the minimal polynomial of α over K. We describe an algorithm for computing
    the local Artin map associated with the extension L / K at a finite or infinite
    prime v of K. We apply this algorithm to decide if a nonzero a ∈ K is a norm from
    L, assuming that L / K is cyclic.
author:
- first_name: Vincenzo
  full_name: Acciaro, Vincenzo
  last_name: Acciaro
- first_name: Jürgen
  full_name: Klüners, Jürgen
  id: '21202'
  last_name: Klüners
citation:
  ama: Acciaro V, Klüners J. Computing Local Artin Maps, and Solvability of Norm Equations.
    <i>Journal of Symbolic Computation</i>. 2000;30(3):239-252. doi:<a href="https://doi.org/10.1006/jsco.2000.0361">10.1006/jsco.2000.0361</a>
  apa: Acciaro, V., &#38; Klüners, J. (2000). Computing Local Artin Maps, and Solvability
    of Norm Equations. <i>Journal of Symbolic Computation</i>, <i>30</i>(3), 239–252.
    <a href="https://doi.org/10.1006/jsco.2000.0361">https://doi.org/10.1006/jsco.2000.0361</a>
  bibtex: '@article{Acciaro_Klüners_2000, title={Computing Local Artin Maps, and Solvability
    of Norm Equations}, volume={30}, DOI={<a href="https://doi.org/10.1006/jsco.2000.0361">10.1006/jsco.2000.0361</a>},
    number={3}, journal={Journal of Symbolic Computation}, publisher={Elsevier BV},
    author={Acciaro, Vincenzo and Klüners, Jürgen}, year={2000}, pages={239–252} }'
  chicago: 'Acciaro, Vincenzo, and Jürgen Klüners. “Computing Local Artin Maps, and
    Solvability of Norm Equations.” <i>Journal of Symbolic Computation</i> 30, no.
    3 (2000): 239–52. <a href="https://doi.org/10.1006/jsco.2000.0361">https://doi.org/10.1006/jsco.2000.0361</a>.'
  ieee: 'V. Acciaro and J. Klüners, “Computing Local Artin Maps, and Solvability of
    Norm Equations,” <i>Journal of Symbolic Computation</i>, vol. 30, no. 3, pp. 239–252,
    2000, doi: <a href="https://doi.org/10.1006/jsco.2000.0361">10.1006/jsco.2000.0361</a>.'
  mla: Acciaro, Vincenzo, and Jürgen Klüners. “Computing Local Artin Maps, and Solvability
    of Norm Equations.” <i>Journal of Symbolic Computation</i>, vol. 30, no. 3, Elsevier
    BV, 2000, pp. 239–52, doi:<a href="https://doi.org/10.1006/jsco.2000.0361">10.1006/jsco.2000.0361</a>.
  short: V. Acciaro, J. Klüners, Journal of Symbolic Computation 30 (2000) 239–252.
date_created: 2022-12-23T09:58:48Z
date_updated: 2023-03-06T09:57:34Z
department:
- _id: '102'
doi: 10.1006/jsco.2000.0361
intvolume: '        30'
issue: '3'
keyword:
- Computational Mathematics
- Algebra and Number Theory
language:
- iso: eng
page: 239-252
publication: Journal of Symbolic Computation
publication_identifier:
  issn:
  - 0747-7171
publication_status: published
publisher: Elsevier BV
status: public
title: Computing Local Artin Maps, and Solvability of Norm Equations
type: journal_article
user_id: '93826'
volume: 30
year: '2000'
...
---
_id: '34899'
abstract:
- lang: eng
  text: We describe methods for the construction of polynomials with certain types
    of Galois groups. As an application we deduce that all transitive groups G up
    to degree 15 occur as Galois groups of regular extensions of ℚ (t), and in each
    case compute a polynomial f ∈ ℚ [ x ] with Gal(f)  = G.
author:
- first_name: Jürgen
  full_name: Klüners, Jürgen
  id: '21202'
  last_name: Klüners
- first_name: Gunter
  full_name: Malle, Gunter
  last_name: Malle
citation:
  ama: Klüners J, Malle G. Explicit Galois Realization of Transitive Groups of Degree
    up to 15. <i>Journal of Symbolic Computation</i>. 2000;30(6):675-716. doi:<a href="https://doi.org/10.1006/jsco.2000.0378">10.1006/jsco.2000.0378</a>
  apa: Klüners, J., &#38; Malle, G. (2000). Explicit Galois Realization of Transitive
    Groups of Degree up to 15. <i>Journal of Symbolic Computation</i>, <i>30</i>(6),
    675–716. <a href="https://doi.org/10.1006/jsco.2000.0378">https://doi.org/10.1006/jsco.2000.0378</a>
  bibtex: '@article{Klüners_Malle_2000, title={Explicit Galois Realization of Transitive
    Groups of Degree up to 15}, volume={30}, DOI={<a href="https://doi.org/10.1006/jsco.2000.0378">10.1006/jsco.2000.0378</a>},
    number={6}, journal={Journal of Symbolic Computation}, publisher={Elsevier BV},
    author={Klüners, Jürgen and Malle, Gunter}, year={2000}, pages={675–716} }'
  chicago: 'Klüners, Jürgen, and Gunter Malle. “Explicit Galois Realization of Transitive
    Groups of Degree up to 15.” <i>Journal of Symbolic Computation</i> 30, no. 6 (2000):
    675–716. <a href="https://doi.org/10.1006/jsco.2000.0378">https://doi.org/10.1006/jsco.2000.0378</a>.'
  ieee: 'J. Klüners and G. Malle, “Explicit Galois Realization of Transitive Groups
    of Degree up to 15,” <i>Journal of Symbolic Computation</i>, vol. 30, no. 6, pp.
    675–716, 2000, doi: <a href="https://doi.org/10.1006/jsco.2000.0378">10.1006/jsco.2000.0378</a>.'
  mla: Klüners, Jürgen, and Gunter Malle. “Explicit Galois Realization of Transitive
    Groups of Degree up to 15.” <i>Journal of Symbolic Computation</i>, vol. 30, no.
    6, Elsevier BV, 2000, pp. 675–716, doi:<a href="https://doi.org/10.1006/jsco.2000.0378">10.1006/jsco.2000.0378</a>.
  short: J. Klüners, G. Malle, Journal of Symbolic Computation 30 (2000) 675–716.
date_created: 2022-12-23T09:57:28Z
date_updated: 2023-03-06T10:48:05Z
department:
- _id: '102'
doi: 10.1006/jsco.2000.0378
intvolume: '        30'
issue: '6'
keyword:
- Computational Mathematics
- Algebra and Number Theory
language:
- iso: eng
page: 675-716
publication: Journal of Symbolic Computation
publication_identifier:
  issn:
  - 0747-7171
publication_status: published
publisher: Elsevier BV
status: public
title: Explicit Galois Realization of Transitive Groups of Degree up to 15
type: journal_article
user_id: '93826'
volume: 30
year: '2000'
...
---
_id: '34898'
abstract:
- lang: eng
  text: We compute a polynomial with Galois group SL₂(11) over ℚ. Furthermore we prove
    that SL₂(11) is the Galois group of a regular extension of ℚ (t).
author:
- first_name: Jürgen
  full_name: Klüners, Jürgen
  id: '21202'
  last_name: Klüners
citation:
  ama: Klüners J. A Polynomial with Galois GroupSL2(11). <i>Journal of Symbolic Computation</i>.
    2000;30(6):733-737. doi:<a href="https://doi.org/10.1006/jsco.2000.0380">10.1006/jsco.2000.0380</a>
  apa: Klüners, J. (2000). A Polynomial with Galois GroupSL2(11). <i>Journal of Symbolic
    Computation</i>, <i>30</i>(6), 733–737. <a href="https://doi.org/10.1006/jsco.2000.0380">https://doi.org/10.1006/jsco.2000.0380</a>
  bibtex: '@article{Klüners_2000, title={A Polynomial with Galois GroupSL2(11)}, volume={30},
    DOI={<a href="https://doi.org/10.1006/jsco.2000.0380">10.1006/jsco.2000.0380</a>},
    number={6}, journal={Journal of Symbolic Computation}, publisher={Elsevier BV},
    author={Klüners, Jürgen}, year={2000}, pages={733–737} }'
  chicago: 'Klüners, Jürgen. “A Polynomial with Galois GroupSL2(11).” <i>Journal of
    Symbolic Computation</i> 30, no. 6 (2000): 733–37. <a href="https://doi.org/10.1006/jsco.2000.0380">https://doi.org/10.1006/jsco.2000.0380</a>.'
  ieee: 'J. Klüners, “A Polynomial with Galois GroupSL2(11),” <i>Journal of Symbolic
    Computation</i>, vol. 30, no. 6, pp. 733–737, 2000, doi: <a href="https://doi.org/10.1006/jsco.2000.0380">10.1006/jsco.2000.0380</a>.'
  mla: Klüners, Jürgen. “A Polynomial with Galois GroupSL2(11).” <i>Journal of Symbolic
    Computation</i>, vol. 30, no. 6, Elsevier BV, 2000, pp. 733–37, doi:<a href="https://doi.org/10.1006/jsco.2000.0380">10.1006/jsco.2000.0380</a>.
  short: J. Klüners, Journal of Symbolic Computation 30 (2000) 733–737.
date_created: 2022-12-23T09:56:52Z
date_updated: 2023-03-06T10:48:40Z
department:
- _id: '102'
doi: 10.1006/jsco.2000.0380
intvolume: '        30'
issue: '6'
keyword:
- Computational Mathematics
- Algebra and Number Theory
language:
- iso: eng
page: 733-737
publication: Journal of Symbolic Computation
publication_identifier:
  issn:
  - 0747-7171
publication_status: published
publisher: Elsevier BV
status: public
title: A Polynomial with Galois GroupSL2(11)
type: journal_article
user_id: '93826'
volume: 30
year: '2000'
...
---
_id: '34902'
abstract:
- lang: eng
  text: We present a new polynomial decomposition which generalizes the functional
    and homogeneous bivariate decomposition of irreducible monic polynomials in one
    variable over the rationals. With these decompositions it is possible to calculate
    the roots of an imprimitive polynomial by solving polynomial equations of lower
    degree.
author:
- first_name: Jürgen
  full_name: Klüners, Jürgen
  id: '21202'
  last_name: Klüners
citation:
  ama: Klüners J. On Polynomial Decompositions. <i>Journal of Symbolic Computation</i>.
    1999;27(3):261-269. doi:<a href="https://doi.org/10.1006/jsco.1998.0252">10.1006/jsco.1998.0252</a>
  apa: Klüners, J. (1999). On Polynomial Decompositions. <i>Journal of Symbolic Computation</i>,
    <i>27</i>(3), 261–269. <a href="https://doi.org/10.1006/jsco.1998.0252">https://doi.org/10.1006/jsco.1998.0252</a>
  bibtex: '@article{Klüners_1999, title={On Polynomial Decompositions}, volume={27},
    DOI={<a href="https://doi.org/10.1006/jsco.1998.0252">10.1006/jsco.1998.0252</a>},
    number={3}, journal={Journal of Symbolic Computation}, publisher={Elsevier BV},
    author={Klüners, Jürgen}, year={1999}, pages={261–269} }'
  chicago: 'Klüners, Jürgen. “On Polynomial Decompositions.” <i>Journal of Symbolic
    Computation</i> 27, no. 3 (1999): 261–69. <a href="https://doi.org/10.1006/jsco.1998.0252">https://doi.org/10.1006/jsco.1998.0252</a>.'
  ieee: 'J. Klüners, “On Polynomial Decompositions,” <i>Journal of Symbolic Computation</i>,
    vol. 27, no. 3, pp. 261–269, 1999, doi: <a href="https://doi.org/10.1006/jsco.1998.0252">10.1006/jsco.1998.0252</a>.'
  mla: Klüners, Jürgen. “On Polynomial Decompositions.” <i>Journal of Symbolic Computation</i>,
    vol. 27, no. 3, Elsevier BV, 1999, pp. 261–69, doi:<a href="https://doi.org/10.1006/jsco.1998.0252">10.1006/jsco.1998.0252</a>.
  short: J. Klüners, Journal of Symbolic Computation 27 (1999) 261–269.
date_created: 2022-12-23T10:01:15Z
date_updated: 2023-03-06T09:21:29Z
department:
- _id: '102'
doi: 10.1006/jsco.1998.0252
intvolume: '        27'
issue: '3'
keyword:
- Computational Mathematics
- Algebra and Number Theory
language:
- iso: eng
page: 261-269
publication: Journal of Symbolic Computation
publication_identifier:
  issn:
  - 0747-7171
publication_status: published
publisher: Elsevier BV
status: public
title: On Polynomial Decompositions
type: journal_article
user_id: '93826'
volume: 27
year: '1999'
...
---
_id: '35941'
abstract:
- lang: eng
  text: "Let L = ℚ(α) be an abelian number field of degree n. Most\r\nalgorithms for
    computing the lattice of subfields of L require the computation\r\nof all the
    conjugates of α. This is usually achieved by factoring the minimal\r\npolynomial
    mα(x) of α over L. In practice, the existing algorithms for factoring\r\npolynomials
    over algebraic number fields can handle only problems of moderate\r\nsize. In
    this paper we describe a fast probabilistic algorithm for computing\r\nthe conjugates
    of α, which is based on p-adic techniques. Given mα(x) and a\r\nrational prime
    p which does not divide the discriminant disc(mα(x)) of mα(x),\r\nthe algorithm
    computes the Frobenius automorphism of p in time polynomial\r\nin the size of
    p and in the size of mα(x). By repeatedly applying the algorithm\r\nto randomly
    chosen primes it is possible to compute all the conjugates of α."
author:
- first_name: Jürgen
  full_name: Klüners, Jürgen
  id: '21202'
  last_name: Klüners
- first_name: Vincenzo
  full_name: Acciaro, Vincenzo
  last_name: Acciaro
citation:
  ama: Klüners J, Acciaro V. Computing Automorphisms of Abelian Number Fields. <i>Mathematics
    of Computation</i>. 1999;68(227):1179-1186.
  apa: Klüners, J., &#38; Acciaro, V. (1999). Computing Automorphisms of Abelian Number
    Fields. <i>Mathematics of Computation</i>, <i>68</i>(227), 1179–1186.
  bibtex: '@article{Klüners_Acciaro_1999, title={Computing Automorphisms of Abelian
    Number Fields}, volume={68}, number={227}, journal={Mathematics of Computation},
    publisher={American Mathematical Society (AMS)}, author={Klüners, Jürgen and Acciaro,
    Vincenzo}, year={1999}, pages={1179–1186} }'
  chicago: 'Klüners, Jürgen, and Vincenzo Acciaro. “Computing Automorphisms of Abelian
    Number Fields.” <i>Mathematics of Computation</i> 68, no. 227 (1999): 1179–86.'
  ieee: J. Klüners and V. Acciaro, “Computing Automorphisms of Abelian Number Fields,”
    <i>Mathematics of Computation</i>, vol. 68, no. 227, pp. 1179–1186, 1999.
  mla: Klüners, Jürgen, and Vincenzo Acciaro. “Computing Automorphisms of Abelian
    Number Fields.” <i>Mathematics of Computation</i>, vol. 68, no. 227, American
    Mathematical Society (AMS), 1999, pp. 1179–86.
  short: J. Klüners, V. Acciaro, Mathematics of Computation 68 (1999) 1179–1186.
date_created: 2023-01-11T09:31:21Z
date_updated: 2023-03-06T10:28:52Z
department:
- _id: '102'
intvolume: '        68'
issue: '227'
language:
- iso: eng
page: 1179-1186
publication: Mathematics of Computation
publication_identifier:
  issn:
  - 1088-6842
  - 0025-5718
publication_status: published
publisher: American Mathematical Society (AMS)
related_material:
  link:
  - relation: confirmation
    url: https://www.ams.org/journals/mcom/1999-68-227/S0025-5718-99-01084-4/S0025-5718-99-01084-4.pdf
status: public
title: Computing Automorphisms of Abelian Number Fields
type: journal_article
user_id: '93826'
volume: 68
year: '1999'
...
---
_id: '34903'
abstract:
- lang: eng
  text: The software packageKANT V4for computations in algebraic number fields is
    now available in version 4. In addition a new user interface has been released.
    We will outline the features of this new software package.
author:
- first_name: M.
  full_name: DABERKOW, M.
  last_name: DABERKOW
- first_name: C.
  full_name: FIEKER, C.
  last_name: FIEKER
- first_name: Jürgen
  full_name: Klüners, Jürgen
  id: '21202'
  last_name: Klüners
- first_name: M.
  full_name: POHST, M.
  last_name: POHST
- first_name: K.
  full_name: ROEGNER, K.
  last_name: ROEGNER
- first_name: M.
  full_name: SCHÖRNIG, M.
  last_name: SCHÖRNIG
- first_name: K.
  full_name: WILDANGER, K.
  last_name: WILDANGER
citation:
  ama: DABERKOW M, FIEKER C, Klüners J, et al. KANT V4. <i>Journal of Symbolic Computation</i>.
    1997;24(3-4):267-283. doi:<a href="https://doi.org/10.1006/jsco.1996.0126">10.1006/jsco.1996.0126</a>
  apa: DABERKOW, M., FIEKER, C., Klüners, J., POHST, M., ROEGNER, K., SCHÖRNIG, M.,
    &#38; WILDANGER, K. (1997). KANT V4. <i>Journal of Symbolic Computation</i>, <i>24</i>(3–4),
    267–283. <a href="https://doi.org/10.1006/jsco.1996.0126">https://doi.org/10.1006/jsco.1996.0126</a>
  bibtex: '@article{DABERKOW_FIEKER_Klüners_POHST_ROEGNER_SCHÖRNIG_WILDANGER_1997,
    title={KANT V4}, volume={24}, DOI={<a href="https://doi.org/10.1006/jsco.1996.0126">10.1006/jsco.1996.0126</a>},
    number={3–4}, journal={Journal of Symbolic Computation}, publisher={Elsevier BV},
    author={DABERKOW, M. and FIEKER, C. and Klüners, Jürgen and POHST, M. and ROEGNER,
    K. and SCHÖRNIG, M. and WILDANGER, K.}, year={1997}, pages={267–283} }'
  chicago: 'DABERKOW, M., C. FIEKER, Jürgen Klüners, M. POHST, K. ROEGNER, M. SCHÖRNIG,
    and K. WILDANGER. “KANT V4.” <i>Journal of Symbolic Computation</i> 24, no. 3–4
    (1997): 267–83. <a href="https://doi.org/10.1006/jsco.1996.0126">https://doi.org/10.1006/jsco.1996.0126</a>.'
  ieee: 'M. DABERKOW <i>et al.</i>, “KANT V4,” <i>Journal of Symbolic Computation</i>,
    vol. 24, no. 3–4, pp. 267–283, 1997, doi: <a href="https://doi.org/10.1006/jsco.1996.0126">10.1006/jsco.1996.0126</a>.'
  mla: DABERKOW, M., et al. “KANT V4.” <i>Journal of Symbolic Computation</i>, vol.
    24, no. 3–4, Elsevier BV, 1997, pp. 267–83, doi:<a href="https://doi.org/10.1006/jsco.1996.0126">10.1006/jsco.1996.0126</a>.
  short: M. DABERKOW, C. FIEKER, J. Klüners, M. POHST, K. ROEGNER, M. SCHÖRNIG, K.
    WILDANGER, Journal of Symbolic Computation 24 (1997) 267–283.
date_created: 2022-12-23T10:02:24Z
date_updated: 2023-03-06T09:23:30Z
ddc:
- '000'
department:
- _id: '102'
doi: 10.1006/jsco.1996.0126
has_accepted_license: '1'
intvolume: '        24'
issue: 3-4
keyword:
- Computational Mathematics
- Algebra and Number Theory
language:
- iso: eng
page: 267-283
publication: Journal of Symbolic Computation
publication_identifier:
  issn:
  - 0747-7171
publication_status: published
publisher: Elsevier BV
status: public
title: KANT V4
type: journal_article
user_id: '93826'
volume: 24
year: '1997'
...
---
_id: '34904'
abstract:
- lang: eng
  text: The purpose of this article is to determine all subfields ℚ(β) of fixed degree
    of a given algebraic number field ℚ(α). It is convenient to describe each subfield
    by a pair (h,g) of polynomials in ℚ[t] resp. Z[t] such thatgis the minimal polynomial
    of β = h(α). The computations are done in unramifiedp-adic extensions and use
    information concerning subgroups of the Galois group of the normal closure of
    ℚ(α) obtained from the van der Waerden criterion.
author:
- first_name: Jürgen
  full_name: Klüners, Jürgen
  id: '21202'
  last_name: Klüners
- first_name: Michael
  full_name: Pohst, Michael
  last_name: Pohst
citation:
  ama: Klüners J, Pohst M. On Computing Subfields. <i>Journal of Symbolic Computation</i>.
    1997;24(3-4):385-397. doi:<a href="https://doi.org/10.1006/jsco.1996.0140">10.1006/jsco.1996.0140</a>
  apa: Klüners, J., &#38; Pohst, M. (1997). On Computing Subfields. <i>Journal of
    Symbolic Computation</i>, <i>24</i>(3–4), 385–397. <a href="https://doi.org/10.1006/jsco.1996.0140">https://doi.org/10.1006/jsco.1996.0140</a>
  bibtex: '@article{Klüners_Pohst_1997, title={On Computing Subfields}, volume={24},
    DOI={<a href="https://doi.org/10.1006/jsco.1996.0140">10.1006/jsco.1996.0140</a>},
    number={3–4}, journal={Journal of Symbolic Computation}, publisher={Elsevier BV},
    author={Klüners, Jürgen and Pohst, Michael}, year={1997}, pages={385–397} }'
  chicago: 'Klüners, Jürgen, and Michael Pohst. “On Computing Subfields.” <i>Journal
    of Symbolic Computation</i> 24, no. 3–4 (1997): 385–97. <a href="https://doi.org/10.1006/jsco.1996.0140">https://doi.org/10.1006/jsco.1996.0140</a>.'
  ieee: 'J. Klüners and M. Pohst, “On Computing Subfields,” <i>Journal of Symbolic
    Computation</i>, vol. 24, no. 3–4, pp. 385–397, 1997, doi: <a href="https://doi.org/10.1006/jsco.1996.0140">10.1006/jsco.1996.0140</a>.'
  mla: Klüners, Jürgen, and Michael Pohst. “On Computing Subfields.” <i>Journal of
    Symbolic Computation</i>, vol. 24, no. 3–4, Elsevier BV, 1997, pp. 385–97, doi:<a
    href="https://doi.org/10.1006/jsco.1996.0140">10.1006/jsco.1996.0140</a>.
  short: J. Klüners, M. Pohst, Journal of Symbolic Computation 24 (1997) 385–397.
date_created: 2022-12-23T10:03:02Z
date_updated: 2023-03-06T10:36:21Z
ddc:
- '000'
department:
- _id: '102'
doi: 10.1006/jsco.1996.0140
has_accepted_license: '1'
intvolume: '        24'
issue: 3-4
keyword:
- Computational Mathematics
- Algebra and Number Theory
language:
- iso: eng
page: 385-397
publication: Journal of Symbolic Computation
publication_identifier:
  issn:
  - 0747-7171
publication_status: published
publisher: Elsevier BV
status: public
title: On Computing Subfields
type: journal_article
user_id: '93826'
volume: 24
year: '1997'
...
---
_id: '42806'
author:
- first_name: Jürgen
  full_name: Klüners, Jürgen
  id: '21202'
  last_name: Klüners
citation:
  ama: Klüners J. <i>Über Die Berechnung von Automorphismen Und Teilkörpern Algebraischer
    Zahlkörper (Dissertation)</i>.; 1997.
  apa: Klüners, J. (1997). <i>Über die Berechnung von Automorphismen und Teilkörpern
    algebraischer Zahlkörper (Dissertation)</i>.
  bibtex: '@book{Klüners_1997, place={TU Berlin}, title={Über die Berechnung von Automorphismen
    und Teilkörpern algebraischer Zahlkörper (Dissertation)}, author={Klüners, Jürgen},
    year={1997} }'
  chicago: Klüners, Jürgen. <i>Über Die Berechnung von Automorphismen Und Teilkörpern
    Algebraischer Zahlkörper (Dissertation)</i>. TU Berlin, 1997.
  ieee: J. Klüners, <i>Über die Berechnung von Automorphismen und Teilkörpern algebraischer
    Zahlkörper (Dissertation)</i>. TU Berlin, 1997.
  mla: Klüners, Jürgen. <i>Über Die Berechnung von Automorphismen Und Teilkörpern
    Algebraischer Zahlkörper (Dissertation)</i>. 1997.
  short: J. Klüners, Über Die Berechnung von Automorphismen Und Teilkörpern Algebraischer
    Zahlkörper (Dissertation), TU Berlin, 1997.
date_created: 2023-03-07T09:00:38Z
date_updated: 2023-03-07T09:24:39Z
department:
- _id: '102'
extern: '1'
language:
- iso: eng
page: '93'
place: TU Berlin
related_material:
  link:
  - relation: confirmation
    url: https://math.uni-paderborn.de/fileadmin/mathematik/AG-Computeralgebra/Publications-klueners/diss.pdf
status: public
title: Über die Berechnung von Automorphismen und Teilkörpern algebraischer Zahlkörper
  (Dissertation)
type: dissertation
user_id: '93826'
year: '1997'
...
---
_id: '42808'
author:
- first_name: Jürgen
  full_name: Klüners, Jürgen
  id: '21202'
  last_name: Klüners
citation:
  ama: Klüners J. <i>Über Die Berechnung von Teilkörpern Algebraischer Zahlkörper
    (Diplomarbeit)</i>.; 1995.
  apa: Klüners, J. (1995). <i>Über die Berechnung von Teilkörpern algebraischer Zahlkörper
    (Diplomarbeit)</i>.
  bibtex: '@book{Klüners_1995, place={TU Berlin}, title={Über die Berechnung von Teilkörpern
    algebraischer Zahlkörper (Diplomarbeit)}, author={Klüners, Jürgen}, year={1995}
    }'
  chicago: Klüners, Jürgen. <i>Über Die Berechnung von Teilkörpern Algebraischer Zahlkörper
    (Diplomarbeit)</i>. TU Berlin, 1995.
  ieee: J. Klüners, <i>Über die Berechnung von Teilkörpern algebraischer Zahlkörper
    (Diplomarbeit)</i>. TU Berlin, 1995.
  mla: Klüners, Jürgen. <i>Über Die Berechnung von Teilkörpern Algebraischer Zahlkörper
    (Diplomarbeit)</i>. 1995.
  short: J. Klüners, Über Die Berechnung von Teilkörpern Algebraischer Zahlkörper
    (Diplomarbeit), TU Berlin, 1995.
date_created: 2023-03-07T09:12:39Z
date_updated: 2023-03-07T09:25:16Z
department:
- _id: '102'
extern: '1'
language:
- iso: eng
page: '91'
place: TU Berlin
related_material:
  link:
  - relation: confirmation
    url: https://math.uni-paderborn.de/fileadmin/mathematik/AG-Computeralgebra/Publications-klueners/diplom.pdf
status: public
title: Über die Berechnung von Teilkörpern algebraischer Zahlkörper (Diplomarbeit)
type: mastersthesis
user_id: '93826'
year: '1995'
...