---
_id: '34841'
abstract:
- lang: eng
  text: "We give an exact formula for the number of G-extensions of local function
    fields Fq((t)) for finite abelian groups G up to a conductor bound. As an application
    we give a lower bound for the corresponding counting problem by discriminant.\r\n"
author:
- first_name: Jürgen
  full_name: Klüners, Jürgen
  id: '21202'
  last_name: Klüners
- first_name: Raphael
  full_name: Müller, Raphael
  last_name: Müller
citation:
  ama: Klüners J, Müller R. The conductor density of local function fields with abelian
    Galois group. <i>Journal of Number Theory</i>. 2020;212:311-322. doi:<a href="https://doi.org/10.1016/j.jnt.2019.11.007">10.1016/j.jnt.2019.11.007</a>
  apa: Klüners, J., &#38; Müller, R. (2020). The conductor density of local function
    fields with abelian Galois group. <i>Journal of Number Theory</i>, <i>212</i>,
    311–322. <a href="https://doi.org/10.1016/j.jnt.2019.11.007">https://doi.org/10.1016/j.jnt.2019.11.007</a>
  bibtex: '@article{Klüners_Müller_2020, title={The conductor density of local function
    fields with abelian Galois group}, volume={212}, DOI={<a href="https://doi.org/10.1016/j.jnt.2019.11.007">10.1016/j.jnt.2019.11.007</a>},
    journal={Journal of Number Theory}, publisher={Elsevier BV}, author={Klüners,
    Jürgen and Müller, Raphael}, year={2020}, pages={311–322} }'
  chicago: 'Klüners, Jürgen, and Raphael Müller. “The Conductor Density of Local Function
    Fields with Abelian Galois Group.” <i>Journal of Number Theory</i> 212 (2020):
    311–22. <a href="https://doi.org/10.1016/j.jnt.2019.11.007">https://doi.org/10.1016/j.jnt.2019.11.007</a>.'
  ieee: 'J. Klüners and R. Müller, “The conductor density of local function fields
    with abelian Galois group,” <i>Journal of Number Theory</i>, vol. 212, pp. 311–322,
    2020, doi: <a href="https://doi.org/10.1016/j.jnt.2019.11.007">10.1016/j.jnt.2019.11.007</a>.'
  mla: Klüners, Jürgen, and Raphael Müller. “The Conductor Density of Local Function
    Fields with Abelian Galois Group.” <i>Journal of Number Theory</i>, vol. 212,
    Elsevier BV, 2020, pp. 311–22, doi:<a href="https://doi.org/10.1016/j.jnt.2019.11.007">10.1016/j.jnt.2019.11.007</a>.
  short: J. Klüners, R. Müller, Journal of Number Theory 212 (2020) 311–322.
date_created: 2022-12-22T10:50:03Z
date_updated: 2025-06-13T08:18:30Z
department:
- _id: '102'
doi: 10.1016/j.jnt.2019.11.007
external_id:
  arxiv:
  - '1904.02573 '
intvolume: '       212'
keyword:
- Algebra and Number Theory
language:
- iso: eng
page: 311-322
publication: Journal of Number Theory
publication_identifier:
  issn:
  - 0022-314X
publication_status: published
publisher: Elsevier BV
status: public
title: The conductor density of local function fields with abelian Galois group
type: journal_article
user_id: '82981'
volume: 212
year: '2020'
...
---
_id: '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: '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: '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: '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'
...