---
_id: '34916'
abstract:
- lang: eng
  text: We describe the powers of irreducible polynomials occurring as characteristic
    polynomials of automorphisms of even unimodular lattices over number fields. This
    generalizes results of Gross & McMullen and Bayer-Fluckiger & Taelman.
author:
- first_name: Markus
  full_name: Kirschmer, Markus
  id: '82258'
  last_name: Kirschmer
citation:
  ama: Kirschmer M. Automorphisms of even unimodular lattices over number fields.
    <i>Journal of Number Theory</i>. 2019;197:121-134. doi:<a href="https://doi.org/10.1016/j.jnt.2018.08.004">10.1016/j.jnt.2018.08.004</a>
  apa: Kirschmer, M. (2019). Automorphisms of even unimodular lattices over number
    fields. <i>Journal of Number Theory</i>, <i>197</i>, 121–134. <a href="https://doi.org/10.1016/j.jnt.2018.08.004">https://doi.org/10.1016/j.jnt.2018.08.004</a>
  bibtex: '@article{Kirschmer_2019, title={Automorphisms of even unimodular lattices
    over number fields}, volume={197}, DOI={<a href="https://doi.org/10.1016/j.jnt.2018.08.004">10.1016/j.jnt.2018.08.004</a>},
    journal={Journal of Number Theory}, publisher={Elsevier BV}, author={Kirschmer,
    Markus}, year={2019}, pages={121–134} }'
  chicago: 'Kirschmer, Markus. “Automorphisms of Even Unimodular Lattices over Number
    Fields.” <i>Journal of Number Theory</i> 197 (2019): 121–34. <a href="https://doi.org/10.1016/j.jnt.2018.08.004">https://doi.org/10.1016/j.jnt.2018.08.004</a>.'
  ieee: 'M. Kirschmer, “Automorphisms of even unimodular lattices over number fields,”
    <i>Journal of Number Theory</i>, vol. 197, pp. 121–134, 2019, doi: <a href="https://doi.org/10.1016/j.jnt.2018.08.004">10.1016/j.jnt.2018.08.004</a>.'
  mla: Kirschmer, Markus. “Automorphisms of Even Unimodular Lattices over Number Fields.”
    <i>Journal of Number Theory</i>, vol. 197, Elsevier BV, 2019, pp. 121–34, doi:<a
    href="https://doi.org/10.1016/j.jnt.2018.08.004">10.1016/j.jnt.2018.08.004</a>.
  short: M. Kirschmer, Journal of Number Theory 197 (2019) 121–134.
date_created: 2022-12-23T11:04:34Z
date_updated: 2023-12-06T10:07:17Z
department:
- _id: '102'
doi: 10.1016/j.jnt.2018.08.004
intvolume: '       197'
keyword:
- Algebra and Number Theory
language:
- iso: eng
page: 121-134
publication: Journal of Number Theory
publication_identifier:
  issn:
  - 0022-314X
publication_status: published
publisher: Elsevier BV
status: public
title: Automorphisms of even unimodular lattices over number fields
type: journal_article
user_id: '82258'
volume: 197
year: '2019'
...
---
_id: '55284'
author:
- first_name: Ch.
  full_name: Elsholtz, Ch.
  last_name: Elsholtz
- first_name: Marc
  full_name: Technau, Marc
  id: '106108'
  last_name: Technau
  orcid: 0000-0001-9650-2459
- first_name: N.
  full_name: Technau, N.
  last_name: Technau
citation:
  ama: Elsholtz Ch, Technau M, Technau N. The maximal order of iterated multiplicative
    functions. <i>Mathematika</i>. 2019;64(4):990–1009. doi:<a href="https://doi.org/10.1112/S0025579319000214">10.1112/S0025579319000214</a>
  apa: Elsholtz, Ch., Technau, M., &#38; Technau, N. (2019). The maximal order of
    iterated multiplicative functions. <i>Mathematika</i>, <i>64</i>(4), 990–1009.
    <a href="https://doi.org/10.1112/S0025579319000214">https://doi.org/10.1112/S0025579319000214</a>
  bibtex: '@article{Elsholtz_Technau_Technau_2019, title={The maximal order of iterated
    multiplicative functions}, volume={64}, DOI={<a href="https://doi.org/10.1112/S0025579319000214">10.1112/S0025579319000214</a>},
    number={4}, journal={Mathematika}, author={Elsholtz, Ch. and Technau, Marc and
    Technau, N.}, year={2019}, pages={990–1009} }'
  chicago: 'Elsholtz, Ch., Marc Technau, and N. Technau. “The Maximal Order of Iterated
    Multiplicative Functions.” <i>Mathematika</i> 64, no. 4 (2019): 990–1009. <a href="https://doi.org/10.1112/S0025579319000214">https://doi.org/10.1112/S0025579319000214</a>.'
  ieee: 'Ch. Elsholtz, M. Technau, and N. Technau, “The maximal order of iterated
    multiplicative functions,” <i>Mathematika</i>, vol. 64, no. 4, pp. 990–1009, 2019,
    doi: <a href="https://doi.org/10.1112/S0025579319000214">10.1112/S0025579319000214</a>.'
  mla: Elsholtz, Ch., et al. “The Maximal Order of Iterated Multiplicative Functions.”
    <i>Mathematika</i>, vol. 64, no. 4, 2019, pp. 990–1009, doi:<a href="https://doi.org/10.1112/S0025579319000214">10.1112/S0025579319000214</a>.
  short: Ch. Elsholtz, M. Technau, N. Technau, Mathematika 64 (2019) 990–1009.
date_created: 2024-07-16T11:09:02Z
date_updated: 2024-07-24T07:25:42Z
department:
- _id: '102'
doi: 10.1112/S0025579319000214
extern: '1'
intvolume: '        64'
issue: '4'
language:
- iso: eng
page: 990–1009
publication: Mathematika
status: public
title: The maximal order of iterated multiplicative functions
type: journal_article
user_id: '106108'
volume: 64
year: '2019'
...
---
_id: '55285'
author:
- first_name: Marc
  full_name: Technau, Marc
  id: '106108'
  last_name: Technau
  orcid: 0000-0001-9650-2459
citation:
  ama: Technau M. Generalised Beatty sets. <i>Notes Number Theory Discrete Math</i>.
    2019;25(2):127–135. doi:<a href="https://doi.org/10.7546/nntdm.2019.25.2.127-135">10.7546/nntdm.2019.25.2.127-135</a>
  apa: Technau, M. (2019). Generalised Beatty sets. <i>Notes Number Theory Discrete
    Math.</i>, <i>25</i>(2), 127–135. <a href="https://doi.org/10.7546/nntdm.2019.25.2.127-135">https://doi.org/10.7546/nntdm.2019.25.2.127-135</a>
  bibtex: '@article{Technau_2019, title={Generalised Beatty sets}, volume={25}, DOI={<a
    href="https://doi.org/10.7546/nntdm.2019.25.2.127-135">10.7546/nntdm.2019.25.2.127-135</a>},
    number={2}, journal={Notes Number Theory Discrete Math.}, author={Technau, Marc},
    year={2019}, pages={127–135} }'
  chicago: 'Technau, Marc. “Generalised Beatty Sets.” <i>Notes Number Theory Discrete
    Math.</i> 25, no. 2 (2019): 127–135. <a href="https://doi.org/10.7546/nntdm.2019.25.2.127-135">https://doi.org/10.7546/nntdm.2019.25.2.127-135</a>.'
  ieee: 'M. Technau, “Generalised Beatty sets,” <i>Notes Number Theory Discrete Math.</i>,
    vol. 25, no. 2, pp. 127–135, 2019, doi: <a href="https://doi.org/10.7546/nntdm.2019.25.2.127-135">10.7546/nntdm.2019.25.2.127-135</a>.'
  mla: Technau, Marc. “Generalised Beatty Sets.” <i>Notes Number Theory Discrete Math.</i>,
    vol. 25, no. 2, 2019, pp. 127–135, doi:<a href="https://doi.org/10.7546/nntdm.2019.25.2.127-135">10.7546/nntdm.2019.25.2.127-135</a>.
  short: M. Technau, Notes Number Theory Discrete Math. 25 (2019) 127–135.
date_created: 2024-07-16T11:09:02Z
date_updated: 2024-07-24T07:25:59Z
department:
- _id: '102'
doi: 10.7546/nntdm.2019.25.2.127-135
extern: '1'
intvolume: '        25'
issue: '2'
language:
- iso: eng
page: 127–135
publication: Notes Number Theory Discrete Math.
status: public
title: Generalised Beatty sets
type: journal_article
user_id: '106108'
volume: 25
year: '2019'
...
---
_id: '34915'
abstract:
- lang: eng
  text: We describe the determinants of the automorphism groups of Hermitian lattices
    over local fields. Using a result of G. Shimura, this yields an explicit method
    to compute the special genera in a given genus of Hermitian lattices over a number
    field.
author:
- first_name: Markus
  full_name: Kirschmer, Markus
  id: '82258'
  last_name: Kirschmer
citation:
  ama: Kirschmer M. Determinant groups of Hermitian lattices over local fields. <i>Archiv
    der Mathematik</i>. 2019;113(4):337-347. doi:<a href="https://doi.org/10.1007/s00013-019-01348-z">10.1007/s00013-019-01348-z</a>
  apa: Kirschmer, M. (2019). Determinant groups of Hermitian lattices over local fields.
    <i>Archiv Der Mathematik</i>, <i>113</i>(4), 337–347. <a href="https://doi.org/10.1007/s00013-019-01348-z">https://doi.org/10.1007/s00013-019-01348-z</a>
  bibtex: '@article{Kirschmer_2019, title={Determinant groups of Hermitian lattices
    over local fields}, volume={113}, DOI={<a href="https://doi.org/10.1007/s00013-019-01348-z">10.1007/s00013-019-01348-z</a>},
    number={4}, journal={Archiv der Mathematik}, publisher={Springer Science and Business
    Media LLC}, author={Kirschmer, Markus}, year={2019}, pages={337–347} }'
  chicago: 'Kirschmer, Markus. “Determinant Groups of Hermitian Lattices over Local
    Fields.” <i>Archiv Der Mathematik</i> 113, no. 4 (2019): 337–47. <a href="https://doi.org/10.1007/s00013-019-01348-z">https://doi.org/10.1007/s00013-019-01348-z</a>.'
  ieee: 'M. Kirschmer, “Determinant groups of Hermitian lattices over local fields,”
    <i>Archiv der Mathematik</i>, vol. 113, no. 4, pp. 337–347, 2019, doi: <a href="https://doi.org/10.1007/s00013-019-01348-z">10.1007/s00013-019-01348-z</a>.'
  mla: Kirschmer, Markus. “Determinant Groups of Hermitian Lattices over Local Fields.”
    <i>Archiv Der Mathematik</i>, vol. 113, no. 4, Springer Science and Business Media
    LLC, 2019, pp. 337–47, doi:<a href="https://doi.org/10.1007/s00013-019-01348-z">10.1007/s00013-019-01348-z</a>.
  short: M. Kirschmer, Archiv Der Mathematik 113 (2019) 337–347.
date_created: 2022-12-23T11:03:41Z
date_updated: 2023-04-04T09:05:04Z
department:
- _id: '102'
doi: 10.1007/s00013-019-01348-z
intvolume: '       113'
issue: '4'
keyword:
- General Mathematics
language:
- iso: eng
page: 337-347
publication: Archiv der Mathematik
publication_identifier:
  issn:
  - 0003-889X
  - 1420-8938
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Determinant groups of Hermitian lattices over local fields
type: journal_article
user_id: '93826'
volume: 113
year: '2019'
...
---
_id: '55291'
author:
- first_name: Marc
  full_name: Technau, Marc
  id: '106108'
  last_name: Technau
  orcid: 0000-0001-9650-2459
citation:
  ama: Technau M. <i>On Beatty Sets and Some Generalisations Thereof</i>. University
    of Würzburg; 2018. doi:<a href="https://doi.org/10.25972/WUP-978-3-95826-089-4">10.25972/WUP-978-3-95826-089-4</a>
  apa: Technau, M. (2018). <i>On Beatty sets and some generalisations thereof</i>.
    University of Würzburg. <a href="https://doi.org/10.25972/WUP-978-3-95826-089-4">https://doi.org/10.25972/WUP-978-3-95826-089-4</a>
  bibtex: '@book{Technau_2018, place={Würzburg}, title={On Beatty sets and some generalisations
    thereof}, DOI={<a href="https://doi.org/10.25972/WUP-978-3-95826-089-4">10.25972/WUP-978-3-95826-089-4</a>},
    publisher={University of Würzburg}, author={Technau, Marc}, year={2018} }'
  chicago: 'Technau, Marc. <i>On Beatty Sets and Some Generalisations Thereof</i>.
    Würzburg: University of Würzburg, 2018. <a href="https://doi.org/10.25972/WUP-978-3-95826-089-4">https://doi.org/10.25972/WUP-978-3-95826-089-4</a>.'
  ieee: 'M. Technau, <i>On Beatty sets and some generalisations thereof</i>. Würzburg:
    University of Würzburg, 2018.'
  mla: Technau, Marc. <i>On Beatty Sets and Some Generalisations Thereof</i>. University
    of Würzburg, 2018, doi:<a href="https://doi.org/10.25972/WUP-978-3-95826-089-4">10.25972/WUP-978-3-95826-089-4</a>.
  short: M. Technau, On Beatty Sets and Some Generalisations Thereof, University of
    Würzburg, Würzburg, 2018.
date_created: 2024-07-16T11:09:19Z
date_updated: 2024-07-24T07:24:57Z
department:
- _id: '102'
doi: 10.25972/WUP-978-3-95826-089-4
extern: '1'
language:
- iso: eng
place: Würzburg
publisher: University of Würzburg
status: public
supervisor:
- first_name: Jörn
  full_name: Steuding, Jörn
  last_name: Steuding
title: On Beatty sets and some generalisations thereof
type: dissertation
user_id: '106108'
year: '2018'
...
---
_id: '34843'
abstract:
- lang: eng
  text: "A polynomial time algorithm to find generators of the lattice of all subfields
    of a given number field was given in van Hoeij et al. (2013).\r\n\r\nThis article
    reports on a massive speedup of this algorithm. This is primary achieved by our
    new concept of Galois-generating subfields. In general this is a very small set
    of subfields that determine all other subfields in a group-theoretic way. We compute
    them by targeted calls to the method from van Hoeij et al. (2013). For an early
    termination of these calls, we give a list of criteria that imply that further
    calls will not result in additional subfields.\r\n\r\nFinally, we explain how
    we use subfields to get a good starting group for the computation of Galois groups."
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
citation:
  ama: Elsenhans A-S, Klüners J. Computing subfields of number fields and applications
    to Galois group computations. <i>Journal of Symbolic Computation</i>. 2018;93:1-20.
    doi:<a href="https://doi.org/10.1016/j.jsc.2018.04.013">10.1016/j.jsc.2018.04.013</a>
  apa: Elsenhans, A.-S., &#38; Klüners, J. (2018). Computing subfields of number fields
    and applications to Galois group computations. <i>Journal of Symbolic Computation</i>,
    <i>93</i>, 1–20. <a href="https://doi.org/10.1016/j.jsc.2018.04.013">https://doi.org/10.1016/j.jsc.2018.04.013</a>
  bibtex: '@article{Elsenhans_Klüners_2018, title={Computing subfields of number fields
    and applications to Galois group computations}, volume={93}, DOI={<a href="https://doi.org/10.1016/j.jsc.2018.04.013">10.1016/j.jsc.2018.04.013</a>},
    journal={Journal of Symbolic Computation}, publisher={Elsevier BV}, author={Elsenhans,
    Andreas-Stephan and Klüners, Jürgen}, year={2018}, pages={1–20} }'
  chicago: 'Elsenhans, Andreas-Stephan, and Jürgen Klüners. “Computing Subfields of
    Number Fields and Applications to Galois Group Computations.” <i>Journal of Symbolic
    Computation</i> 93 (2018): 1–20. <a href="https://doi.org/10.1016/j.jsc.2018.04.013">https://doi.org/10.1016/j.jsc.2018.04.013</a>.'
  ieee: 'A.-S. Elsenhans and J. Klüners, “Computing subfields of number fields and
    applications to Galois group computations,” <i>Journal of Symbolic Computation</i>,
    vol. 93, pp. 1–20, 2018, doi: <a href="https://doi.org/10.1016/j.jsc.2018.04.013">10.1016/j.jsc.2018.04.013</a>.'
  mla: Elsenhans, Andreas-Stephan, and Jürgen Klüners. “Computing Subfields of Number
    Fields and Applications to Galois Group Computations.” <i>Journal of Symbolic
    Computation</i>, vol. 93, Elsevier BV, 2018, pp. 1–20, doi:<a href="https://doi.org/10.1016/j.jsc.2018.04.013">10.1016/j.jsc.2018.04.013</a>.
  short: A.-S. Elsenhans, J. Klüners, Journal of Symbolic Computation 93 (2018) 1–20.
date_created: 2022-12-22T10:52:18Z
date_updated: 2023-03-06T09:05:51Z
department:
- _id: '102'
doi: 10.1016/j.jsc.2018.04.013
external_id:
  arxiv:
  - '1610.06837 '
intvolume: '        93'
keyword:
- Computational Mathematics
- Algebra and Number Theory
language:
- iso: eng
page: 1-20
publication: Journal of Symbolic Computation
publication_identifier:
  issn:
  - 0747-7171
publication_status: published
publisher: Elsevier BV
status: public
title: Computing subfields of number fields and applications to Galois group computations
type: journal_article
user_id: '93826'
volume: 93
year: '2018'
...
---
_id: '42788'
abstract:
- lang: eng
  text: We classify all one-class genera of admissible lattice chains of length at
    least 2 in hermitian spaces over number fields. If L is a lattice in the chain
    and p the prime ideal dividing the index of the lattices in the chain, then the
    {p}-arithmetic group Aut(L{p}) acts chamber transitively on the corresponding
    Bruhat-Tits building. So our classification provides a step forward to a complete
    classification of these chamber transitive groups which has been announced 1987
    (without a detailed proof) by Kantor, Liebler and Tits. In fact we find all their
    groups over number fields and one additional building with a discrete chamber
    transitive group.
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. One Class Genera of Lattice Chains Over Number Fields.
    In: <i>Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory</i>.
    Springer International Publishing; 2018. doi:<a href="https://doi.org/10.1007/978-3-319-70566-8_22">10.1007/978-3-319-70566-8_22</a>'
  apa: Kirschmer, M., &#38; Nebe, G. (2018). One Class Genera of Lattice Chains Over
    Number Fields. In <i>Algorithmic and Experimental Methods in Algebra, Geometry,
    and Number Theory</i>. Springer International Publishing. <a href="https://doi.org/10.1007/978-3-319-70566-8_22">https://doi.org/10.1007/978-3-319-70566-8_22</a>
  bibtex: '@inbook{Kirschmer_Nebe_2018, place={Cham}, title={One Class Genera of Lattice
    Chains Over Number Fields}, DOI={<a href="https://doi.org/10.1007/978-3-319-70566-8_22">10.1007/978-3-319-70566-8_22</a>},
    booktitle={Algorithmic and Experimental Methods in Algebra, Geometry, and Number
    Theory}, publisher={Springer International Publishing}, author={Kirschmer, Markus
    and Nebe, Gabriele}, year={2018} }'
  chicago: 'Kirschmer, Markus, and Gabriele Nebe. “One Class Genera of Lattice Chains
    Over Number Fields.” In <i>Algorithmic and Experimental Methods in Algebra, Geometry,
    and Number Theory</i>. Cham: Springer International Publishing, 2018. <a href="https://doi.org/10.1007/978-3-319-70566-8_22">https://doi.org/10.1007/978-3-319-70566-8_22</a>.'
  ieee: 'M. Kirschmer and G. Nebe, “One Class Genera of Lattice Chains Over Number
    Fields,” in <i>Algorithmic and Experimental Methods in Algebra, Geometry, and
    Number Theory</i>, Cham: Springer International Publishing, 2018.'
  mla: Kirschmer, Markus, and Gabriele Nebe. “One Class Genera of Lattice Chains Over
    Number Fields.” <i>Algorithmic and Experimental Methods in Algebra, Geometry,
    and Number Theory</i>, Springer International Publishing, 2018, doi:<a href="https://doi.org/10.1007/978-3-319-70566-8_22">10.1007/978-3-319-70566-8_22</a>.
  short: 'M. Kirschmer, G. Nebe, in: Algorithmic and Experimental Methods in Algebra,
    Geometry, and Number Theory, Springer International Publishing, Cham, 2018.'
date_created: 2023-03-07T08:23:48Z
date_updated: 2023-04-04T09:08:19Z
department:
- _id: '102'
doi: 10.1007/978-3-319-70566-8_22
extern: '1'
language:
- iso: eng
place: Cham
publication: Algorithmic and Experimental Methods in Algebra, Geometry, and Number
  Theory
publication_identifier:
  isbn:
  - '9783319705651'
  - '9783319705668'
publication_status: published
publisher: Springer International Publishing
status: public
title: One Class Genera of Lattice Chains Over Number Fields
type: book_chapter
user_id: '93826'
year: '2018'
...
---
_id: '42790'
abstract:
- lang: eng
  text: We show that exceptional algebraic groups over number fields do not admit
    one-class genera of parahoric groups, except in the case G₂ . For the group G₂,
    we enumerate all such one-class genera for the usual seven-dimensional representation.
author:
- first_name: Markus
  full_name: Kirschmer, Markus
  id: '82258'
  last_name: Kirschmer
citation:
  ama: Kirschmer M. One-class genera of exceptional groups over number fields. <i>Journal
    de Théorie des Nombres de Bordeaux</i>. 2018;30(3):847-857. doi:<a href="https://doi.org/10.5802/jtnb.1052">10.5802/jtnb.1052</a>
  apa: Kirschmer, M. (2018). One-class genera of exceptional groups over number fields.
    <i>Journal de Théorie Des Nombres de Bordeaux</i>, <i>30</i>(3), 847–857. <a href="https://doi.org/10.5802/jtnb.1052">https://doi.org/10.5802/jtnb.1052</a>
  bibtex: '@article{Kirschmer_2018, title={One-class genera of exceptional groups
    over number fields}, volume={30}, DOI={<a href="https://doi.org/10.5802/jtnb.1052">10.5802/jtnb.1052</a>},
    number={3}, journal={Journal de Théorie des Nombres de Bordeaux}, publisher={Cellule
    MathDoc/CEDRAM}, author={Kirschmer, Markus}, year={2018}, pages={847–857} }'
  chicago: 'Kirschmer, Markus. “One-Class Genera of Exceptional Groups over Number
    Fields.” <i>Journal de Théorie Des Nombres de Bordeaux</i> 30, no. 3 (2018): 847–57.
    <a href="https://doi.org/10.5802/jtnb.1052">https://doi.org/10.5802/jtnb.1052</a>.'
  ieee: 'M. Kirschmer, “One-class genera of exceptional groups over number fields,”
    <i>Journal de Théorie des Nombres de Bordeaux</i>, vol. 30, no. 3, pp. 847–857,
    2018, doi: <a href="https://doi.org/10.5802/jtnb.1052">10.5802/jtnb.1052</a>.'
  mla: Kirschmer, Markus. “One-Class Genera of Exceptional Groups over Number Fields.”
    <i>Journal de Théorie Des Nombres de Bordeaux</i>, vol. 30, no. 3, Cellule MathDoc/CEDRAM,
    2018, pp. 847–57, doi:<a href="https://doi.org/10.5802/jtnb.1052">10.5802/jtnb.1052</a>.
  short: M. Kirschmer, Journal de Théorie Des Nombres de Bordeaux 30 (2018) 847–857.
date_created: 2023-03-07T08:27:36Z
date_updated: 2023-04-04T09:07:32Z
department:
- _id: '102'
doi: 10.5802/jtnb.1052
extern: '1'
intvolume: '        30'
issue: '3'
keyword:
- Algebra and Number Theory
language:
- iso: eng
page: 847-857
publication: Journal de Théorie des Nombres de Bordeaux
publication_identifier:
  issn:
  - 1246-7405
  - 2118-8572
publication_status: published
publisher: Cellule MathDoc/CEDRAM
status: public
title: One-class genera of exceptional groups over number fields
type: journal_article
user_id: '93826'
volume: 30
year: '2018'
...
---
_id: '55293'
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. <i>Emptiness Problems
    for Integer Circuits</i>.; 2017.
  apa: Barth, D., Beck, M., Dose, T., Glaßer, Ch., Michler, L., &#38; Technau, M.
    (2017). <i>Emptiness problems for integer circuits</i>.
  bibtex: '@book{Barth_Beck_Dose_Glaßer_Michler_Technau_2017, place={https://eccc.weizmann.ac.il/report/2017/012},
    title={Emptiness problems for integer circuits}, author={Barth, D. and Beck, M.
    and Dose, T. and Glaßer, Ch. and Michler, L. and Technau, Marc}, year={2017} }'
  chicago: Barth, D., M. Beck, T. Dose, Ch. Glaßer, L. Michler, and Marc Technau.
    <i>Emptiness Problems for Integer Circuits</i>. https://eccc.weizmann.ac.il/report/2017/012,
    2017.
  ieee: D. Barth, M. Beck, T. Dose, Ch. Glaßer, L. Michler, and M. Technau, <i>Emptiness
    problems for integer circuits</i>. https://eccc.weizmann.ac.il/report/2017/012,
    2017.
  mla: Barth, D., et al. <i>Emptiness Problems for Integer Circuits</i>. 2017.
  short: D. Barth, M. Beck, T. Dose, Ch. Glaßer, L. Michler, M. Technau, Emptiness
    Problems for Integer Circuits, https://eccc.weizmann.ac.il/report/2017/012, 2017.
date_created: 2024-07-16T11:09:20Z
date_updated: 2024-07-24T07:24:26Z
department:
- _id: '102'
extern: '1'
language:
- iso: eng
place: https://eccc.weizmann.ac.il/report/2017/012
status: public
title: Emptiness problems for integer circuits
type: report
user_id: '106108'
year: '2017'
...
---
_id: '55292'
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. In: Larsen KG, Bodlaender HL, Raskin J-F, eds. <i>42nd International
    Symposium on Mathematical Foundations of Computer Science (MFCS 2017)</i>. Vol
    83. Leibniz International Proceedings in Informatics (LIPIcs). Schloss Dagstuhl–Leibniz-Zentrum
    für Informatik; 2017:33:1–33:14. doi:<a href="https://doi.org/10.4230/LIPIcs.MFCS.2017.33">10.4230/LIPIcs.MFCS.2017.33</a>'
  apa: Barth, D., Beck, M., Dose, T., Glaßer, Ch., Michler, L., &#38; Technau, M.
    (2017). Emptiness problems for integer circuits. In K. G. Larsen, H. L. Bodlaender,
    &#38; J.-F. Raskin (Eds.), <i>42nd International Symposium on Mathematical Foundations
    of Computer Science (MFCS 2017)</i> (Vol. 83, p. 33:1–33:14). Schloss Dagstuhl–Leibniz-Zentrum
    für Informatik. <a href="https://doi.org/10.4230/LIPIcs.MFCS.2017.33">https://doi.org/10.4230/LIPIcs.MFCS.2017.33</a>
  bibtex: '@inproceedings{Barth_Beck_Dose_Glaßer_Michler_Technau_2017, series={Leibniz
    International Proceedings in Informatics (LIPIcs)}, title={Emptiness problems
    for integer circuits}, volume={83}, DOI={<a href="https://doi.org/10.4230/LIPIcs.MFCS.2017.33">10.4230/LIPIcs.MFCS.2017.33</a>},
    booktitle={42nd International Symposium on Mathematical Foundations of Computer
    Science (MFCS 2017)}, publisher={Schloss Dagstuhl–Leibniz-Zentrum für Informatik},
    author={Barth, D. and Beck, M. and Dose, T. and Glaßer, Ch. and Michler, L. and
    Technau, Marc}, editor={Larsen, Kim G. and Bodlaender, Hans L. and Raskin, Jean-Francois},
    year={2017}, pages={33:1–33:14}, collection={Leibniz International Proceedings
    in Informatics (LIPIcs)} }'
  chicago: Barth, D., M. Beck, T. Dose, Ch. Glaßer, L. Michler, and Marc Technau.
    “Emptiness Problems for Integer Circuits.” In <i>42nd International Symposium
    on Mathematical Foundations of Computer Science (MFCS 2017)</i>, edited by Kim
    G. Larsen, Hans L. Bodlaender, and Jean-Francois Raskin, 83:33:1–33:14. Leibniz
    International Proceedings in Informatics (LIPIcs). Schloss Dagstuhl–Leibniz-Zentrum
    für Informatik, 2017. <a href="https://doi.org/10.4230/LIPIcs.MFCS.2017.33">https://doi.org/10.4230/LIPIcs.MFCS.2017.33</a>.
  ieee: 'D. Barth, M. Beck, T. Dose, Ch. Glaßer, L. Michler, and M. Technau, “Emptiness
    problems for integer circuits,” in <i>42nd International Symposium on Mathematical
    Foundations of Computer Science (MFCS 2017)</i>, 2017, vol. 83, p. 33:1–33:14,
    doi: <a href="https://doi.org/10.4230/LIPIcs.MFCS.2017.33">10.4230/LIPIcs.MFCS.2017.33</a>.'
  mla: Barth, D., et al. “Emptiness Problems for Integer Circuits.” <i>42nd International
    Symposium on Mathematical Foundations of Computer Science (MFCS 2017)</i>, edited
    by Kim G. Larsen et al., vol. 83, Schloss Dagstuhl–Leibniz-Zentrum für Informatik,
    2017, p. 33:1–33:14, doi:<a href="https://doi.org/10.4230/LIPIcs.MFCS.2017.33">10.4230/LIPIcs.MFCS.2017.33</a>.
  short: 'D. Barth, M. Beck, T. Dose, Ch. Glaßer, L. Michler, M. Technau, in: K.G.
    Larsen, H.L. Bodlaender, J.-F. Raskin (Eds.), 42nd International Symposium on
    Mathematical Foundations of Computer Science (MFCS 2017), Schloss Dagstuhl–Leibniz-Zentrum
    für Informatik, 2017, p. 33:1–33:14.'
date_created: 2024-07-16T11:09:20Z
date_updated: 2024-07-24T07:25:35Z
department:
- _id: '102'
doi: 10.4230/LIPIcs.MFCS.2017.33
editor:
- first_name: Kim G.
  full_name: Larsen, Kim G.
  last_name: Larsen
- first_name: Hans L.
  full_name: Bodlaender, Hans L.
  last_name: Bodlaender
- first_name: Jean-Francois
  full_name: Raskin, Jean-Francois
  last_name: Raskin
extern: '1'
intvolume: '        83'
language:
- iso: eng
page: 33:1–33:14
publication: 42nd International Symposium on Mathematical Foundations of Computer
  Science (MFCS 2017)
publisher: Schloss Dagstuhl–Leibniz-Zentrum für Informatik
series_title: Leibniz International Proceedings in Informatics (LIPIcs)
status: public
title: Emptiness problems for integer circuits
type: conference
user_id: '106108'
volume: 83
year: '2017'
...
---
_id: '55275'
author:
- first_name: Marc
  full_name: Technau, Marc
  id: '106108'
  last_name: Technau
  orcid: 0000-0001-9650-2459
- first_name: N.
  full_name: Technau, N.
  last_name: Technau
citation:
  ama: Technau M, Technau N. A Loewner equation for infinitely many slits. <i>Comput
    Methods Funct Theory</i>. 2017;17(2):255–272. doi:<a href="https://doi.org/10.1007/s40315-016-0179-6">10.1007/s40315-016-0179-6</a>
  apa: Technau, M., &#38; Technau, N. (2017). A Loewner equation for infinitely many
    slits. <i>Comput. Methods Funct. Theory</i>, <i>17</i>(2), 255–272. <a href="https://doi.org/10.1007/s40315-016-0179-6">https://doi.org/10.1007/s40315-016-0179-6</a>
  bibtex: '@article{Technau_Technau_2017, title={A Loewner equation for infinitely
    many slits}, volume={17}, DOI={<a href="https://doi.org/10.1007/s40315-016-0179-6">10.1007/s40315-016-0179-6</a>},
    number={2}, journal={Comput. Methods Funct. Theory}, author={Technau, Marc and
    Technau, N.}, year={2017}, pages={255–272} }'
  chicago: 'Technau, Marc, and N. Technau. “A Loewner Equation for Infinitely Many
    Slits.” <i>Comput. Methods Funct. Theory</i> 17, no. 2 (2017): 255–272. <a href="https://doi.org/10.1007/s40315-016-0179-6">https://doi.org/10.1007/s40315-016-0179-6</a>.'
  ieee: 'M. Technau and N. Technau, “A Loewner equation for infinitely many slits,”
    <i>Comput. Methods Funct. Theory</i>, vol. 17, no. 2, pp. 255–272, 2017, doi:
    <a href="https://doi.org/10.1007/s40315-016-0179-6">10.1007/s40315-016-0179-6</a>.'
  mla: Technau, Marc, and N. Technau. “A Loewner Equation for Infinitely Many Slits.”
    <i>Comput. Methods Funct. Theory</i>, vol. 17, no. 2, 2017, pp. 255–272, doi:<a
    href="https://doi.org/10.1007/s40315-016-0179-6">10.1007/s40315-016-0179-6</a>.
  short: M. Technau, N. Technau, Comput. Methods Funct. Theory 17 (2017) 255–272.
date_created: 2024-07-16T11:08:06Z
date_updated: 2024-07-24T07:24:37Z
department:
- _id: '102'
doi: 10.1007/s40315-016-0179-6
intvolume: '        17'
issue: '2'
language:
- iso: eng
page: 255–272
publication: Comput. Methods Funct. Theory
status: public
title: A Loewner equation for infinitely many slits
type: journal_article
user_id: '106108'
volume: 17
year: '2017'
...
---
_id: '42791'
abstract:
- lang: eng
  text: We describe a practical algorithm to solve the constructive membership problem
    for discrete two-generator subgroups of SL₂(R) or PSL₂(R). This algorithm has
    been implemented in Magma for groups defined over real algebraic number fields.
author:
- first_name: Markus
  full_name: Kirschmer, Markus
  id: '82258'
  last_name: Kirschmer
- first_name: Marion G.
  full_name: Rüther, Marion G.
  last_name: Rüther
citation:
  ama: Kirschmer M, Rüther MG. The constructive membership problem for discrete two-generator
    subgroups of SL(2,R). <i>Journal of Algebra</i>. 2017;480:519-548. doi:<a href="https://doi.org/10.1016/j.jalgebra.2017.02.029">10.1016/j.jalgebra.2017.02.029</a>
  apa: Kirschmer, M., &#38; Rüther, M. G. (2017). The constructive membership problem
    for discrete two-generator subgroups of SL(2,R). <i>Journal of Algebra</i>, <i>480</i>,
    519–548. <a href="https://doi.org/10.1016/j.jalgebra.2017.02.029">https://doi.org/10.1016/j.jalgebra.2017.02.029</a>
  bibtex: '@article{Kirschmer_Rüther_2017, title={The constructive membership problem
    for discrete two-generator subgroups of SL(2,R)}, volume={480}, DOI={<a href="https://doi.org/10.1016/j.jalgebra.2017.02.029">10.1016/j.jalgebra.2017.02.029</a>},
    journal={Journal of Algebra}, publisher={Elsevier BV}, author={Kirschmer, Markus
    and Rüther, Marion G.}, year={2017}, pages={519–548} }'
  chicago: 'Kirschmer, Markus, and Marion G. Rüther. “The Constructive Membership
    Problem for Discrete Two-Generator Subgroups of SL(2,R).” <i>Journal of Algebra</i>
    480 (2017): 519–48. <a href="https://doi.org/10.1016/j.jalgebra.2017.02.029">https://doi.org/10.1016/j.jalgebra.2017.02.029</a>.'
  ieee: 'M. Kirschmer and M. G. Rüther, “The constructive membership problem for discrete
    two-generator subgroups of SL(2,R),” <i>Journal of Algebra</i>, vol. 480, pp.
    519–548, 2017, doi: <a href="https://doi.org/10.1016/j.jalgebra.2017.02.029">10.1016/j.jalgebra.2017.02.029</a>.'
  mla: Kirschmer, Markus, and Marion G. Rüther. “The Constructive Membership Problem
    for Discrete Two-Generator Subgroups of SL(2,R).” <i>Journal of Algebra</i>, vol.
    480, Elsevier BV, 2017, pp. 519–48, doi:<a href="https://doi.org/10.1016/j.jalgebra.2017.02.029">10.1016/j.jalgebra.2017.02.029</a>.
  short: M. Kirschmer, M.G. Rüther, Journal of Algebra 480 (2017) 519–548.
date_created: 2023-03-07T08:28:11Z
date_updated: 2023-04-04T09:10:14Z
department:
- _id: '102'
doi: 10.1016/j.jalgebra.2017.02.029
extern: '1'
intvolume: '       480'
keyword:
- Algebra and Number Theory
language:
- iso: eng
page: 519-548
publication: Journal of Algebra
publication_identifier:
  issn:
  - 0021-8693
publication_status: published
publisher: Elsevier BV
status: public
title: The constructive membership problem for discrete two-generator subgroups of
  SL(2,R)
type: journal_article
user_id: '93826'
volume: 480
year: '2017'
...
---
_id: '55281'
author:
- first_name: J.
  full_name: Steuding, J.
  last_name: Steuding
- first_name: Marc
  full_name: Technau, Marc
  id: '106108'
  last_name: Technau
  orcid: 0000-0001-9650-2459
citation:
  ama: Steuding J, Technau M. The least prime number in a Beatty sequence. <i>J Number
    Theory</i>. 2016;169:144–159. doi:<a href="https://doi.org/10.1016/j.jnt.2016.05.022">10.1016/j.jnt.2016.05.022</a>
  apa: Steuding, J., &#38; Technau, M. (2016). The least prime number in a Beatty
    sequence. <i>J. Number Theory</i>, <i>169</i>, 144–159. <a href="https://doi.org/10.1016/j.jnt.2016.05.022">https://doi.org/10.1016/j.jnt.2016.05.022</a>
  bibtex: '@article{Steuding_Technau_2016, title={The least prime number in a Beatty
    sequence}, volume={169}, DOI={<a href="https://doi.org/10.1016/j.jnt.2016.05.022">10.1016/j.jnt.2016.05.022</a>},
    journal={J. Number Theory}, author={Steuding, J. and Technau, Marc}, year={2016},
    pages={144–159} }'
  chicago: 'Steuding, J., and Marc Technau. “The Least Prime Number in a Beatty Sequence.”
    <i>J. Number Theory</i> 169 (2016): 144–159. <a href="https://doi.org/10.1016/j.jnt.2016.05.022">https://doi.org/10.1016/j.jnt.2016.05.022</a>.'
  ieee: 'J. Steuding and M. Technau, “The least prime number in a Beatty sequence,”
    <i>J. Number Theory</i>, vol. 169, pp. 144–159, 2016, doi: <a href="https://doi.org/10.1016/j.jnt.2016.05.022">10.1016/j.jnt.2016.05.022</a>.'
  mla: Steuding, J., and Marc Technau. “The Least Prime Number in a Beatty Sequence.”
    <i>J. Number Theory</i>, vol. 169, 2016, pp. 144–159, doi:<a href="https://doi.org/10.1016/j.jnt.2016.05.022">10.1016/j.jnt.2016.05.022</a>.
  short: J. Steuding, M. Technau, J. Number Theory 169 (2016) 144–159.
date_created: 2024-07-16T11:09:01Z
date_updated: 2024-07-24T07:26:27Z
department:
- _id: '102'
doi: 10.1016/j.jnt.2016.05.022
extern: '1'
intvolume: '       169'
language:
- iso: eng
page: 144–159
publication: J. Number Theory
status: public
title: The least prime number in a Beatty sequence
type: journal_article
user_id: '106108'
volume: 169
year: '2016'
...
---
_id: '34844'
abstract:
- lang: eng
  text: 'Let k be a number field, K/k a finite Galois extension with Galois group
    G, χ a faithful character of G. We prove that the Artin L-function L(s,χ,K/k)
    determines the Galois closure of K over $\ℚ$. In the special case $k=\ℚ$ it also
    determines the character χ. '
author:
- first_name: Jürgen
  full_name: Klüners, Jürgen
  id: '21202'
  last_name: Klüners
- first_name: Florin
  full_name: Nicolae, Florin
  last_name: Nicolae
citation:
  ama: Klüners J, Nicolae F. Are number fields determined by Artin L-functions? <i>Journal
    of Number Theory</i>. 2016;167:161-168. doi:<a href="https://doi.org/10.1016/j.jnt.2016.03.023">10.1016/j.jnt.2016.03.023</a>
  apa: Klüners, J., &#38; Nicolae, F. (2016). Are number fields determined by Artin
    L-functions? <i>Journal of Number Theory</i>, <i>167</i>, 161–168. <a href="https://doi.org/10.1016/j.jnt.2016.03.023">https://doi.org/10.1016/j.jnt.2016.03.023</a>
  bibtex: '@article{Klüners_Nicolae_2016, title={Are number fields determined by Artin
    L-functions?}, volume={167}, DOI={<a href="https://doi.org/10.1016/j.jnt.2016.03.023">10.1016/j.jnt.2016.03.023</a>},
    journal={Journal of Number Theory}, publisher={Elsevier BV}, author={Klüners,
    Jürgen and Nicolae, Florin}, year={2016}, pages={161–168} }'
  chicago: 'Klüners, Jürgen, and Florin Nicolae. “Are Number Fields Determined by
    Artin L-Functions?” <i>Journal of Number Theory</i> 167 (2016): 161–68. <a href="https://doi.org/10.1016/j.jnt.2016.03.023">https://doi.org/10.1016/j.jnt.2016.03.023</a>.'
  ieee: 'J. Klüners and F. Nicolae, “Are number fields determined by Artin L-functions?,”
    <i>Journal of Number Theory</i>, vol. 167, pp. 161–168, 2016, doi: <a href="https://doi.org/10.1016/j.jnt.2016.03.023">10.1016/j.jnt.2016.03.023</a>.'
  mla: Klüners, Jürgen, and Florin Nicolae. “Are Number Fields Determined by Artin
    L-Functions?” <i>Journal of Number Theory</i>, vol. 167, Elsevier BV, 2016, pp.
    161–68, doi:<a href="https://doi.org/10.1016/j.jnt.2016.03.023">10.1016/j.jnt.2016.03.023</a>.
  short: J. Klüners, F. Nicolae, Journal of Number Theory 167 (2016) 161–168.
date_created: 2022-12-22T10:52:47Z
date_updated: 2023-03-06T10:44:22Z
department:
- _id: '102'
doi: 10.1016/j.jnt.2016.03.023
external_id:
  arxiv:
  - '1509.06883 '
intvolume: '       167'
keyword:
- Algebra and Number Theory
language:
- iso: eng
page: 161-168
publication: Journal of Number Theory
publication_identifier:
  issn:
  - 0022-314X
publication_status: published
publisher: Elsevier BV
status: public
title: Are number fields determined by Artin L-functions?
type: journal_article
user_id: '93826'
volume: 167
year: '2016'
...
---
_id: '42792'
abstract:
- lang: eng
  text: We enumerate all positive definite ternary quadratic forms over number fields
    with class number at most 2. This is done by constructing all definite quaternion
    orders of type number at most 2 over number fields. Finally, we list all definite
    quaternion orders of ideal class number 1 or 2.
author:
- first_name: Markus
  full_name: Kirschmer, Markus
  id: '82258'
  last_name: Kirschmer
- first_name: David
  full_name: Lorch, David
  last_name: Lorch
citation:
  ama: Kirschmer M, Lorch D. Ternary quadratic forms over number fields with small
    class number. <i>Journal of Number Theory</i>. 2016;161:343-361. doi:<a href="https://doi.org/10.1016/j.jnt.2014.11.001">10.1016/j.jnt.2014.11.001</a>
  apa: Kirschmer, M., &#38; Lorch, D. (2016). Ternary quadratic forms over number
    fields with small class number. <i>Journal of Number Theory</i>, <i>161</i>, 343–361.
    <a href="https://doi.org/10.1016/j.jnt.2014.11.001">https://doi.org/10.1016/j.jnt.2014.11.001</a>
  bibtex: '@article{Kirschmer_Lorch_2016, title={Ternary quadratic forms over number
    fields with small class number}, volume={161}, DOI={<a href="https://doi.org/10.1016/j.jnt.2014.11.001">10.1016/j.jnt.2014.11.001</a>},
    journal={Journal of Number Theory}, publisher={Elsevier BV}, author={Kirschmer,
    Markus and Lorch, David}, year={2016}, pages={343–361} }'
  chicago: 'Kirschmer, Markus, and David Lorch. “Ternary Quadratic Forms over Number
    Fields with Small Class Number.” <i>Journal of Number Theory</i> 161 (2016): 343–61.
    <a href="https://doi.org/10.1016/j.jnt.2014.11.001">https://doi.org/10.1016/j.jnt.2014.11.001</a>.'
  ieee: 'M. Kirschmer and D. Lorch, “Ternary quadratic forms over number fields with
    small class number,” <i>Journal of Number Theory</i>, vol. 161, pp. 343–361, 2016,
    doi: <a href="https://doi.org/10.1016/j.jnt.2014.11.001">10.1016/j.jnt.2014.11.001</a>.'
  mla: Kirschmer, Markus, and David Lorch. “Ternary Quadratic Forms over Number Fields
    with Small Class Number.” <i>Journal of Number Theory</i>, vol. 161, Elsevier
    BV, 2016, pp. 343–61, doi:<a href="https://doi.org/10.1016/j.jnt.2014.11.001">10.1016/j.jnt.2014.11.001</a>.
  short: M. Kirschmer, D. Lorch, Journal of Number Theory 161 (2016) 343–361.
date_created: 2023-03-07T08:28:46Z
date_updated: 2023-04-04T09:10:42Z
department:
- _id: '102'
doi: 10.1016/j.jnt.2014.11.001
extern: '1'
intvolume: '       161'
keyword:
- Algebra and Number Theory
language:
- iso: eng
page: 343-361
publication: Journal of Number Theory
publication_identifier:
  issn:
  - 0022-314X
publication_status: published
publisher: Elsevier BV
status: public
title: Ternary quadratic forms over number fields with small class number
type: journal_article
user_id: '93826'
volume: 161
year: '2016'
...
---
_id: '43454'
abstract:
- lang: eng
  text: 'Die Gitter von Klassenzahl eins oder zwei sind hier verfügbar: http://www.math.rwth-aachen.de/~Markus.Kirschmer/forms/'
author:
- first_name: Markus
  full_name: Kirschmer, Markus
  id: '82258'
  last_name: Kirschmer
citation:
  ama: Kirschmer M. <i>Definite Quadratic and Hermitian Forms with Small Class Number
    (Habilitation)</i>.; 2016.
  apa: Kirschmer, M. (2016). <i>Definite quadratic and hermitian forms with small
    class number (Habilitation)</i>.
  bibtex: '@book{Kirschmer_2016, place={RWTH Aachen University}, title={Definite quadratic
    and hermitian forms with small class number (Habilitation)}, author={Kirschmer,
    Markus}, year={2016} }'
  chicago: Kirschmer, Markus. <i>Definite Quadratic and Hermitian Forms with Small
    Class Number (Habilitation)</i>. RWTH Aachen University, 2016.
  ieee: M. Kirschmer, <i>Definite quadratic and hermitian forms with small class number
    (Habilitation)</i>. RWTH Aachen University, 2016.
  mla: Kirschmer, Markus. <i>Definite Quadratic and Hermitian Forms with Small Class
    Number (Habilitation)</i>. 2016.
  short: M. Kirschmer, Definite Quadratic and Hermitian Forms with Small Class Number
    (Habilitation), RWTH Aachen University, 2016.
date_created: 2023-04-11T08:06:35Z
date_updated: 2023-04-11T08:11:20Z
department:
- _id: '102'
extern: '1'
language:
- iso: eng
page: '166'
place: RWTH Aachen University
status: public
title: Definite quadratic and hermitian forms with small class number (Habilitation)
type: misc
user_id: '93826'
year: '2016'
...
---
_id: '34845'
abstract:
- lang: eng
  text: Computational Galois theory, in particular the problem of computing the Galois
    group of a given polynomial, is a very old problem. Currently, the best algorithmic
    solution is Stauduhar’s method. Computationally, one of the key challenges in
    the application of Stauduhar’s method is to find, for a given pair of groups H<G,
    a G-relative H-invariant, that is a multivariate polynomial F that is H-invariant,
    but not G-invariant. While generic, theoretical methods are known to find such
    F, in general they yield impractical answers. We give a general method for computing
    invariants of large degree which improves on previous known methods, as well as
    various special invariants that are derived from the structure of the groups.
    We then apply our new invariants to the task of computing the Galois groups of
    polynomials over the rational numbers, resulting in the first practical degree
    independent algorithm.
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. Computation of Galois groups of rational polynomials.
    <i>LMS Journal of Computation and Mathematics</i>. 2014;17(1):141-158. doi:<a
    href="https://doi.org/10.1112/s1461157013000302">10.1112/s1461157013000302</a>
  apa: Fieker, C., &#38; Klüners, J. (2014). Computation of Galois groups of rational
    polynomials. <i>LMS Journal of Computation and Mathematics</i>, <i>17</i>(1),
    141–158. <a href="https://doi.org/10.1112/s1461157013000302">https://doi.org/10.1112/s1461157013000302</a>
  bibtex: '@article{Fieker_Klüners_2014, title={Computation of Galois groups of rational
    polynomials}, volume={17}, DOI={<a href="https://doi.org/10.1112/s1461157013000302">10.1112/s1461157013000302</a>},
    number={1}, journal={LMS Journal of Computation and Mathematics}, publisher={Wiley},
    author={Fieker, Claus and Klüners, Jürgen}, year={2014}, pages={141–158} }'
  chicago: 'Fieker, Claus, and Jürgen Klüners. “Computation of Galois Groups of Rational
    Polynomials.” <i>LMS Journal of Computation and Mathematics</i> 17, no. 1 (2014):
    141–58. <a href="https://doi.org/10.1112/s1461157013000302">https://doi.org/10.1112/s1461157013000302</a>.'
  ieee: 'C. Fieker and J. Klüners, “Computation of Galois groups of rational polynomials,”
    <i>LMS Journal of Computation and Mathematics</i>, vol. 17, no. 1, pp. 141–158,
    2014, doi: <a href="https://doi.org/10.1112/s1461157013000302">10.1112/s1461157013000302</a>.'
  mla: Fieker, Claus, and Jürgen Klüners. “Computation of Galois Groups of Rational
    Polynomials.” <i>LMS Journal of Computation and Mathematics</i>, vol. 17, no.
    1, Wiley, 2014, pp. 141–58, doi:<a href="https://doi.org/10.1112/s1461157013000302">10.1112/s1461157013000302</a>.
  short: C. Fieker, J. Klüners, LMS Journal of Computation and Mathematics 17 (2014)
    141–158.
date_created: 2022-12-22T10:53:44Z
date_updated: 2023-03-06T09:43:56Z
department:
- _id: '102'
doi: 10.1112/s1461157013000302
external_id:
  arxiv:
  - '1211.3588'
intvolume: '        17'
issue: '1'
keyword:
- Computational Theory and Mathematics
- General Mathematics
language:
- iso: eng
page: 141-158
publication: LMS Journal of Computation and Mathematics
publication_identifier:
  issn:
  - 1461-1570
publication_status: published
publisher: Wiley
status: public
title: Computation of Galois groups of rational polynomials
type: journal_article
user_id: '93826'
volume: 17
year: '2014'
...
---
_id: '42793'
abstract:
- lang: eng
  text: Suppose Q is a definite quadratic form on a vector space V over some totally
    real field K ≠ Q. Then the maximal integral Zₖ-lattices in (V,Q) are locally isometric
    everywhere and hence form a single genus. We enumerate all orthogonal spaces (V,Q)
    of dimension at least 3, where the corresponding genus of maximal integral lattices
    consists of a single isometry class. It turns out, there are 471 such genera.
    Moreover, the dimension of V and the degree of K are bounded by 6 and 5 respectively.
    This classification also yields all maximal quaternion orders of type number one.
author:
- first_name: Markus
  full_name: Kirschmer, Markus
  id: '82258'
  last_name: Kirschmer
citation:
  ama: Kirschmer M. One-class genera of maximal integral quadratic forms. <i>Journal
    of Number Theory</i>. 2014;136:375-393. doi:<a href="https://doi.org/10.1016/j.jnt.2013.10.007">10.1016/j.jnt.2013.10.007</a>
  apa: Kirschmer, M. (2014). One-class genera of maximal integral quadratic forms.
    <i>Journal of Number Theory</i>, <i>136</i>, 375–393. <a href="https://doi.org/10.1016/j.jnt.2013.10.007">https://doi.org/10.1016/j.jnt.2013.10.007</a>
  bibtex: '@article{Kirschmer_2014, title={One-class genera of maximal integral quadratic
    forms}, volume={136}, DOI={<a href="https://doi.org/10.1016/j.jnt.2013.10.007">10.1016/j.jnt.2013.10.007</a>},
    journal={Journal of Number Theory}, publisher={Elsevier BV}, author={Kirschmer,
    Markus}, year={2014}, pages={375–393} }'
  chicago: 'Kirschmer, Markus. “One-Class Genera of Maximal Integral Quadratic Forms.”
    <i>Journal of Number Theory</i> 136 (2014): 375–93. <a href="https://doi.org/10.1016/j.jnt.2013.10.007">https://doi.org/10.1016/j.jnt.2013.10.007</a>.'
  ieee: 'M. Kirschmer, “One-class genera of maximal integral quadratic forms,” <i>Journal
    of Number Theory</i>, vol. 136, pp. 375–393, 2014, doi: <a href="https://doi.org/10.1016/j.jnt.2013.10.007">10.1016/j.jnt.2013.10.007</a>.'
  mla: Kirschmer, Markus. “One-Class Genera of Maximal Integral Quadratic Forms.”
    <i>Journal of Number Theory</i>, vol. 136, Elsevier BV, 2014, pp. 375–93, doi:<a
    href="https://doi.org/10.1016/j.jnt.2013.10.007">10.1016/j.jnt.2013.10.007</a>.
  short: M. Kirschmer, Journal of Number Theory 136 (2014) 375–393.
date_created: 2023-03-07T08:29:34Z
date_updated: 2023-04-04T09:13:29Z
department:
- _id: '102'
doi: 10.1016/j.jnt.2013.10.007
extern: '1'
intvolume: '       136'
keyword:
- Algebra and Number Theory
language:
- iso: eng
page: 375-393
publication: Journal of Number Theory
publication_identifier:
  issn:
  - 0022-314X
publication_status: published
publisher: Elsevier BV
status: public
title: One-class genera of maximal integral quadratic forms
type: journal_article
user_id: '93826'
volume: 136
year: '2014'
...
---
_id: '42801'
abstract:
- lang: eng
  text: We exhibit a practical algorithm for solving the constructive membership problem
    for discrete free subgroups of rank 2 in PSL₂(R) or SL₂(R). This algorithm, together
    with methods for checking whether a two-generator subgroup of PSL₂(R) or SL₂(R)
    is discrete and free, have been implemented in Magma for groups defined over real
    algebraic number fields.
author:
- first_name: Markus
  full_name: Kirschmer, Markus
  id: '82258'
  last_name: Kirschmer
- first_name: CHARLES
  full_name: LEEDHAM-GREEN, CHARLES
  last_name: LEEDHAM-GREEN
citation:
  ama: Kirschmer M, LEEDHAM-GREEN C. Computing with subgroups of the modular group
    . <i>Glasgow Mathematical Journal</i>. 2014;57(1):173-180. doi:<a href="https://doi.org/10.1017/s0017089514000202">10.1017/s0017089514000202</a>
  apa: Kirschmer, M., &#38; LEEDHAM-GREEN, C. (2014). Computing with subgroups of
    the modular group . <i>Glasgow Mathematical Journal</i>, <i>57</i>(1), 173–180.
    <a href="https://doi.org/10.1017/s0017089514000202">https://doi.org/10.1017/s0017089514000202</a>
  bibtex: '@article{Kirschmer_LEEDHAM-GREEN_2014, title={Computing with subgroups
    of the modular group }, volume={57}, DOI={<a href="https://doi.org/10.1017/s0017089514000202">10.1017/s0017089514000202</a>},
    number={1}, journal={Glasgow Mathematical Journal}, publisher={Cambridge University
    Press (CUP)}, author={Kirschmer, Markus and LEEDHAM-GREEN, CHARLES}, year={2014},
    pages={173–180} }'
  chicago: 'Kirschmer, Markus, and CHARLES LEEDHAM-GREEN. “Computing with Subgroups
    of the Modular Group .” <i>Glasgow Mathematical Journal</i> 57, no. 1 (2014):
    173–80. <a href="https://doi.org/10.1017/s0017089514000202">https://doi.org/10.1017/s0017089514000202</a>.'
  ieee: 'M. Kirschmer and C. LEEDHAM-GREEN, “Computing with subgroups of the modular
    group ,” <i>Glasgow Mathematical Journal</i>, vol. 57, no. 1, pp. 173–180, 2014,
    doi: <a href="https://doi.org/10.1017/s0017089514000202">10.1017/s0017089514000202</a>.'
  mla: Kirschmer, Markus, and CHARLES LEEDHAM-GREEN. “Computing with Subgroups of
    the Modular Group .” <i>Glasgow Mathematical Journal</i>, vol. 57, no. 1, Cambridge
    University Press (CUP), 2014, pp. 173–80, doi:<a href="https://doi.org/10.1017/s0017089514000202">10.1017/s0017089514000202</a>.
  short: M. Kirschmer, C. LEEDHAM-GREEN, Glasgow Mathematical Journal 57 (2014) 173–180.
date_created: 2023-03-07T08:47:42Z
date_updated: 2023-04-04T07:55:16Z
department:
- _id: '102'
doi: 10.1017/s0017089514000202
extern: '1'
intvolume: '        57'
issue: '1'
keyword:
- General Mathematics
language:
- iso: eng
page: 173-180
publication: Glasgow Mathematical Journal
publication_identifier:
  issn:
  - 0017-0895
  - 1469-509X
publication_status: published
publisher: Cambridge University Press (CUP)
status: public
title: 'Computing with subgroups of the modular group '
type: journal_article
user_id: '93826'
volume: 57
year: '2014'
...
---
_id: '42794'
abstract:
- lang: eng
  text: We exhibit a practical algorithm for solving the constructive membership problem
    for discrete free subgroups of rank 2 in PSL₂(R) or SL₂(R). This algorithm, together
    with methods for checking whether a two-generator subgroup of PSL₂(R) or SL₂(R)
    is discrete and free, have been implemented in Magma for groups defined over real
    algebraic number fields.
author:
- first_name: B.
  full_name: Eick, B.
  last_name: Eick
- first_name: Markus
  full_name: Kirschmer, Markus
  id: '82258'
  last_name: Kirschmer
- first_name: C.
  full_name: Leedham-Green, C.
  last_name: Leedham-Green
citation:
  ama: Eick B, Kirschmer M, Leedham-Green C. The constructive membership problem for
    discrete free subgroups of rank 2 of SL₂(R). <i>LMS Journal of Computation and
    Mathematics</i>. 2014;17(1):345-359. doi:<a href="https://doi.org/10.1112/s1461157014000047">10.1112/s1461157014000047</a>
  apa: Eick, B., Kirschmer, M., &#38; Leedham-Green, C. (2014). The constructive membership
    problem for discrete free subgroups of rank 2 of SL₂(R). <i>LMS Journal of Computation
    and Mathematics</i>, <i>17</i>(1), 345–359. <a href="https://doi.org/10.1112/s1461157014000047">https://doi.org/10.1112/s1461157014000047</a>
  bibtex: '@article{Eick_Kirschmer_Leedham-Green_2014, title={The constructive membership
    problem for discrete free subgroups of rank 2 of SL₂(R)}, volume={17}, DOI={<a
    href="https://doi.org/10.1112/s1461157014000047">10.1112/s1461157014000047</a>},
    number={1}, journal={LMS Journal of Computation and Mathematics}, publisher={Wiley},
    author={Eick, B. and Kirschmer, Markus and Leedham-Green, C.}, year={2014}, pages={345–359}
    }'
  chicago: 'Eick, B., Markus Kirschmer, and C. Leedham-Green. “The Constructive Membership
    Problem for Discrete Free Subgroups of Rank 2 of SL₂(R).” <i>LMS Journal of Computation
    and Mathematics</i> 17, no. 1 (2014): 345–59. <a href="https://doi.org/10.1112/s1461157014000047">https://doi.org/10.1112/s1461157014000047</a>.'
  ieee: 'B. Eick, M. Kirschmer, and C. Leedham-Green, “The constructive membership
    problem for discrete free subgroups of rank 2 of SL₂(R),” <i>LMS Journal of Computation
    and Mathematics</i>, vol. 17, no. 1, pp. 345–359, 2014, doi: <a href="https://doi.org/10.1112/s1461157014000047">10.1112/s1461157014000047</a>.'
  mla: Eick, B., et al. “The Constructive Membership Problem for Discrete Free Subgroups
    of Rank 2 of SL₂(R).” <i>LMS Journal of Computation and Mathematics</i>, vol.
    17, no. 1, Wiley, 2014, pp. 345–59, doi:<a href="https://doi.org/10.1112/s1461157014000047">10.1112/s1461157014000047</a>.
  short: B. Eick, M. Kirschmer, C. Leedham-Green, LMS Journal of Computation and Mathematics
    17 (2014) 345–359.
date_created: 2023-03-07T08:30:15Z
date_updated: 2023-04-04T09:31:17Z
department:
- _id: '102'
doi: 10.1112/s1461157014000047
extern: '1'
intvolume: '        17'
issue: '1'
keyword:
- Computational Theory and Mathematics
- General Mathematics
language:
- iso: eng
page: 345-359
publication: LMS Journal of Computation and Mathematics
publication_identifier:
  issn:
  - 1461-1570
publication_status: published
publisher: Wiley
status: public
title: The constructive membership problem for discrete free subgroups of rank 2 of
  SL₂(R)
type: journal_article
user_id: '93826'
volume: 17
year: '2014'
...