---
_id: '64181'
abstract:
- lang: eng
  text: "<p>\r\n                    Let\r\n                    <inline-formula content-type=\"math/mathml\">\r\n
    \                     <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"
    alttext=\"upper G\">\r\n                        <mml:semantics>\r\n                          <mml:mi>G</mml:mi>\r\n
    \                         <mml:annotation encoding=\"application/x-tex\">G</mml:annotation>\r\n
    \                       </mml:semantics>\r\n                      </mml:math>\r\n
    \                   </inline-formula>\r\n                    be a finite abelian\r\n
    \                   <inline-formula content-type=\"math/mathml\">\r\n                      <mml:math
    xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"p\">\r\n                        <mml:semantics>\r\n
    \                         <mml:mi>p</mml:mi>\r\n                          <mml:annotation
    encoding=\"application/x-tex\">p</mml:annotation>\r\n                        </mml:semantics>\r\n
    \                     </mml:math>\r\n                    </inline-formula>\r\n
    \                   -group. We count étale\r\n                    <inline-formula
    content-type=\"math/mathml\">\r\n                      <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"
    alttext=\"upper G\">\r\n                        <mml:semantics>\r\n                          <mml:mi>G</mml:mi>\r\n
    \                         <mml:annotation encoding=\"application/x-tex\">G</mml:annotation>\r\n
    \                       </mml:semantics>\r\n                      </mml:math>\r\n
    \                   </inline-formula>\r\n                    -extensions of global
    rational function fields\r\n                    <inline-formula content-type=\"math/mathml\">\r\n
    \                     <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"
    alttext=\"double-struck upper F Subscript q Baseline left-parenthesis upper T
    right-parenthesis\">\r\n                        <mml:semantics>\r\n                          <mml:mrow>\r\n
    \                           <mml:msub>\r\n                              <mml:mrow
    class=\"MJX-TeXAtom-ORD\">\r\n                                <mml:mi mathvariant=\"double-struck\">F</mml:mi>\r\n
    \                             </mml:mrow>\r\n                              <mml:mi>q</mml:mi>\r\n
    \                           </mml:msub>\r\n                            <mml:mo
    stretchy=\"false\">(</mml:mo>\r\n                            <mml:mi>T</mml:mi>\r\n
    \                           <mml:mo stretchy=\"false\">)</mml:mo>\r\n                          </mml:mrow>\r\n
    \                         <mml:annotation encoding=\"application/x-tex\">\\mathbb
    F_q(T)</mml:annotation>\r\n                        </mml:semantics>\r\n                      </mml:math>\r\n
    \                   </inline-formula>\r\n                    of characteristic\r\n
    \                   <inline-formula content-type=\"math/mathml\">\r\n                      <mml:math
    xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"p\">\r\n                        <mml:semantics>\r\n
    \                         <mml:mi>p</mml:mi>\r\n                          <mml:annotation
    encoding=\"application/x-tex\">p</mml:annotation>\r\n                        </mml:semantics>\r\n
    \                     </mml:math>\r\n                    </inline-formula>\r\n
    \                   by the degree of what we call their Artin–Schreier conductor.
    The corresponding (ordinary) generating function turns out to be rational. This
    gives an exact answer to the counting problem, and seems to beg for a geometric
    interpretation.\r\n                  </p>\r\n                  <p>This is in contrast
    with the generating functions for the ordinary conductor (from class field theory)
    and the discriminant, which in general have no meromorphic continuation to the
    entire complex plane.</p>"
author:
- first_name: Fabian
  full_name: Gundlach, Fabian
  id: '100450'
  last_name: Gundlach
citation:
  ama: Gundlach F. Counting abelian extensions by Artin–Schreier conductor. <i>Proceedings
    of the American Mathematical Society</i>. Published online 2025. doi:<a href="https://doi.org/10.1090/proc/17440">10.1090/proc/17440</a>
  apa: Gundlach, F. (2025). Counting abelian extensions by Artin–Schreier conductor.
    <i>Proceedings of the American Mathematical Society</i>. <a href="https://doi.org/10.1090/proc/17440">https://doi.org/10.1090/proc/17440</a>
  bibtex: '@article{Gundlach_2025, title={Counting abelian extensions by Artin–Schreier
    conductor}, DOI={<a href="https://doi.org/10.1090/proc/17440">10.1090/proc/17440</a>},
    journal={Proceedings of the American Mathematical Society}, publisher={American
    Mathematical Society (AMS)}, author={Gundlach, Fabian}, year={2025} }'
  chicago: Gundlach, Fabian. “Counting Abelian Extensions by Artin–Schreier Conductor.”
    <i>Proceedings of the American Mathematical Society</i>, 2025. <a href="https://doi.org/10.1090/proc/17440">https://doi.org/10.1090/proc/17440</a>.
  ieee: 'F. Gundlach, “Counting abelian extensions by Artin–Schreier conductor,” <i>Proceedings
    of the American Mathematical Society</i>, 2025, doi: <a href="https://doi.org/10.1090/proc/17440">10.1090/proc/17440</a>.'
  mla: Gundlach, Fabian. “Counting Abelian Extensions by Artin–Schreier Conductor.”
    <i>Proceedings of the American Mathematical Society</i>, American Mathematical
    Society (AMS), 2025, doi:<a href="https://doi.org/10.1090/proc/17440">10.1090/proc/17440</a>.
  short: F. Gundlach, Proceedings of the American Mathematical Society (2025).
date_created: 2026-02-16T13:00:54Z
date_updated: 2026-02-16T13:01:13Z
doi: 10.1090/proc/17440
language:
- iso: eng
publication: Proceedings of the American Mathematical Society
publication_identifier:
  issn:
  - 1088-6826
  - 0002-9939
publication_status: published
publisher: American Mathematical Society (AMS)
status: public
title: Counting abelian extensions by Artin–Schreier conductor
type: journal_article
user_id: '100450'
year: '2025'
...
---
_id: '63258'
abstract:
- lang: eng
  text: <p>This manuscript studies a no-flux initial-boundary value problem for a
    four-component chemotaxis system that has been proposed as a model for the response
    of cytotoxic T-lymphocytes to a solid tumor. In contrast to classical Keller-Segel
    type situations focusing on two-component interplay of chemotaxing populations
    with a signal directly secreted by themselves, the presently considered system
    accounts for a certain indirect mechanism of attractant evolution. Despite the
    presence of a zero-order exciting nonlinearity of quadratic type that forms a
    core mathematical feature of the model, the manuscript asserts the global existence
    of classical solutions for initial data of arbitrary size in three-dimensional
    domains.</p>
author:
- first_name: Youshan
  full_name: Tao, Youshan
  last_name: Tao
- first_name: Michael
  full_name: Winkler, Michael
  id: '31496'
  last_name: Winkler
citation:
  ama: Tao Y, Winkler M. Global smooth solutions in a chemotaxis system modeling immune
    response to a solid tumor. <i>Proceedings of the American Mathematical Society</i>.
    2024;152(10):4325-4341. doi:<a href="https://doi.org/10.1090/proc/16867">10.1090/proc/16867</a>
  apa: Tao, Y., &#38; Winkler, M. (2024). Global smooth solutions in a chemotaxis
    system modeling immune response to a solid tumor. <i>Proceedings of the American
    Mathematical Society</i>, <i>152</i>(10), 4325–4341. <a href="https://doi.org/10.1090/proc/16867">https://doi.org/10.1090/proc/16867</a>
  bibtex: '@article{Tao_Winkler_2024, title={Global smooth solutions in a chemotaxis
    system modeling immune response to a solid tumor}, volume={152}, DOI={<a href="https://doi.org/10.1090/proc/16867">10.1090/proc/16867</a>},
    number={10}, journal={Proceedings of the American Mathematical Society}, publisher={American
    Mathematical Society (AMS)}, author={Tao, Youshan and Winkler, Michael}, year={2024},
    pages={4325–4341} }'
  chicago: 'Tao, Youshan, and Michael Winkler. “Global Smooth Solutions in a Chemotaxis
    System Modeling Immune Response to a Solid Tumor.” <i>Proceedings of the American
    Mathematical Society</i> 152, no. 10 (2024): 4325–41. <a href="https://doi.org/10.1090/proc/16867">https://doi.org/10.1090/proc/16867</a>.'
  ieee: 'Y. Tao and M. Winkler, “Global smooth solutions in a chemotaxis system modeling
    immune response to a solid tumor,” <i>Proceedings of the American Mathematical
    Society</i>, vol. 152, no. 10, pp. 4325–4341, 2024, doi: <a href="https://doi.org/10.1090/proc/16867">10.1090/proc/16867</a>.'
  mla: Tao, Youshan, and Michael Winkler. “Global Smooth Solutions in a Chemotaxis
    System Modeling Immune Response to a Solid Tumor.” <i>Proceedings of the American
    Mathematical Society</i>, vol. 152, no. 10, American Mathematical Society (AMS),
    2024, pp. 4325–41, doi:<a href="https://doi.org/10.1090/proc/16867">10.1090/proc/16867</a>.
  short: Y. Tao, M. Winkler, Proceedings of the American Mathematical Society 152
    (2024) 4325–4341.
date_created: 2025-12-18T19:07:03Z
date_updated: 2025-12-18T20:14:30Z
doi: 10.1090/proc/16867
intvolume: '       152'
issue: '10'
language:
- iso: eng
page: 4325-4341
publication: Proceedings of the American Mathematical Society
publication_identifier:
  issn:
  - 0002-9939
  - 1088-6826
publication_status: published
publisher: American Mathematical Society (AMS)
status: public
title: Global smooth solutions in a chemotaxis system modeling immune response to
  a solid tumor
type: journal_article
user_id: '31496'
volume: 152
year: '2024'
...
---
_id: '34839'
abstract:
- lang: eng
  text: We describe the relations among the ℓ-torsion conjecture, a conjecture of
    Malle giving an upper bound for the number of extensions, and the discriminant
    multiplicity conjecture. We prove that the latter two conjectures are equivalent
    in some sense. Altogether, the three conjectures are equivalent for the class
    of solvable groups. We then prove the ℓ-torsion conjecture for ℓ-groups and the
    other two conjectures for nilpotent groups.
author:
- first_name: Jürgen
  full_name: Klüners, Jürgen
  id: '21202'
  last_name: Klüners
- first_name: Jiuya
  full_name: Wang, Jiuya
  last_name: Wang
citation:
  ama: Klüners J, Wang J. ℓ-torsion bounds for the class group of number fields with
    an ℓ-group as Galois group. <i>Proceedings of the American Mathematical Society</i>.
    2022;150(7):2793-2805. doi:<a href="https://doi.org/10.1090/proc/15882">10.1090/proc/15882</a>
  apa: Klüners, J., &#38; Wang, J. (2022). ℓ-torsion bounds for the class group of
    number fields with an ℓ-group as Galois group. <i>Proceedings of the American
    Mathematical Society</i>, <i>150</i>(7), 2793–2805. <a href="https://doi.org/10.1090/proc/15882">https://doi.org/10.1090/proc/15882</a>
  bibtex: '@article{Klüners_Wang_2022, title={ℓ-torsion bounds for the class group
    of number fields with an ℓ-group as Galois group}, volume={150}, DOI={<a href="https://doi.org/10.1090/proc/15882">10.1090/proc/15882</a>},
    number={7}, journal={Proceedings of the American Mathematical Society}, publisher={American
    Mathematical Society (AMS)}, author={Klüners, Jürgen and Wang, Jiuya}, year={2022},
    pages={2793–2805} }'
  chicago: 'Klüners, Jürgen, and Jiuya Wang. “ℓ-Torsion Bounds for the Class Group
    of Number Fields with an ℓ-Group as Galois Group.” <i>Proceedings of the American
    Mathematical Society</i> 150, no. 7 (2022): 2793–2805. <a href="https://doi.org/10.1090/proc/15882">https://doi.org/10.1090/proc/15882</a>.'
  ieee: 'J. Klüners and J. Wang, “ℓ-torsion bounds for the class group of number fields
    with an ℓ-group as Galois group,” <i>Proceedings of the American Mathematical
    Society</i>, vol. 150, no. 7, pp. 2793–2805, 2022, doi: <a href="https://doi.org/10.1090/proc/15882">10.1090/proc/15882</a>.'
  mla: Klüners, Jürgen, and Jiuya Wang. “ℓ-Torsion Bounds for the Class Group of Number
    Fields with an ℓ-Group as Galois Group.” <i>Proceedings of the American Mathematical
    Society</i>, vol. 150, no. 7, American Mathematical Society (AMS), 2022, pp. 2793–805,
    doi:<a href="https://doi.org/10.1090/proc/15882">10.1090/proc/15882</a>.
  short: J. Klüners, J. Wang, Proceedings of the American Mathematical Society 150
    (2022) 2793–2805.
date_created: 2022-12-22T10:47:01Z
date_updated: 2023-03-06T08:47:42Z
department:
- _id: '102'
doi: 10.1090/proc/15882
external_id:
  arxiv:
  - '2003.12161 '
intvolume: '       150'
issue: '7'
keyword:
- Applied Mathematics
- General Mathematics
language:
- iso: eng
page: 2793-2805
publication: Proceedings of the American Mathematical Society
publication_identifier:
  issn:
  - 0002-9939
  - 1088-6826
publication_status: published
publisher: American Mathematical Society (AMS)
status: public
title: ℓ-torsion bounds for the class group of number fields with an ℓ-group as Galois
  group
type: journal_article
user_id: '93826'
volume: 150
year: '2022'
...
---
_id: '37659'
author:
- first_name: Margit
  full_name: Rösler, Margit
  id: '37390'
  last_name: Rösler
- first_name: Michael
  full_name: Voit, Michael
  last_name: Voit
citation:
  ama: Rösler M, Voit M. Positive intertwiners for Bessel functions of type B. <i>Proceedings
    of the American Mathematical Society</i>. 2021;149(3):1151-1163. doi:<a href="https://doi.org/10.1090/proc/15312">10.1090/proc/15312</a>
  apa: Rösler, M., &#38; Voit, M. (2021). Positive intertwiners for Bessel functions
    of type B. <i>Proceedings of the American Mathematical Society</i>, <i>149</i>(3),
    1151–1163. <a href="https://doi.org/10.1090/proc/15312">https://doi.org/10.1090/proc/15312</a>
  bibtex: '@article{Rösler_Voit_2021, title={Positive intertwiners for Bessel functions
    of type B}, volume={149}, DOI={<a href="https://doi.org/10.1090/proc/15312">10.1090/proc/15312</a>},
    number={3}, journal={Proceedings of the American Mathematical Society}, publisher={American
    Mathematical Society (AMS)}, author={Rösler, Margit and Voit, Michael}, year={2021},
    pages={1151–1163} }'
  chicago: 'Rösler, Margit, and Michael Voit. “Positive Intertwiners for Bessel Functions
    of Type B.” <i>Proceedings of the American Mathematical Society</i> 149, no. 3
    (2021): 1151–63. <a href="https://doi.org/10.1090/proc/15312">https://doi.org/10.1090/proc/15312</a>.'
  ieee: 'M. Rösler and M. Voit, “Positive intertwiners for Bessel functions of type
    B,” <i>Proceedings of the American Mathematical Society</i>, vol. 149, no. 3,
    pp. 1151–1163, 2021, doi: <a href="https://doi.org/10.1090/proc/15312">10.1090/proc/15312</a>.'
  mla: Rösler, Margit, and Michael Voit. “Positive Intertwiners for Bessel Functions
    of Type B.” <i>Proceedings of the American Mathematical Society</i>, vol. 149,
    no. 3, American Mathematical Society (AMS), 2021, pp. 1151–63, doi:<a href="https://doi.org/10.1090/proc/15312">10.1090/proc/15312</a>.
  short: M. Rösler, M. Voit, Proceedings of the American Mathematical Society 149
    (2021) 1151–1163.
date_created: 2023-01-20T09:22:12Z
date_updated: 2023-01-24T22:16:16Z
department:
- _id: '555'
doi: 10.1090/proc/15312
intvolume: '       149'
issue: '3'
keyword:
- Applied Mathematics
- General Mathematics
language:
- iso: eng
page: 1151-1163
publication: Proceedings of the American Mathematical Society
publication_identifier:
  issn:
  - 0002-9939
  - 1088-6826
publication_status: published
publisher: American Mathematical Society (AMS)
status: public
title: Positive intertwiners for Bessel functions of type B
type: journal_article
user_id: '37390'
volume: 149
year: '2021'
...
---
_id: '40666'
author:
- first_name: Margit
  full_name: Rösler, Margit
  id: '37390'
  last_name: Rösler
- first_name: Michael
  full_name: Voit, Michael
  last_name: Voit
citation:
  ama: Rösler M, Voit M. An uncertainty principle for Hankel transforms. <i>Proceedings
    of the American Mathematical Society</i>. 1999;127(1):183–194.
  apa: Rösler, M., &#38; Voit, M. (1999). An uncertainty principle for Hankel transforms.
    <i>Proceedings of the American Mathematical Society</i>, <i>127</i>(1), 183–194.
  bibtex: '@article{Rösler_Voit_1999, title={An uncertainty principle for Hankel transforms},
    volume={127}, number={1}, journal={Proceedings of the American Mathematical Society},
    publisher={American Mathematical Society (AMS)}, author={Rösler, Margit and Voit,
    Michael}, year={1999}, pages={183–194} }'
  chicago: 'Rösler, Margit, and Michael Voit. “An Uncertainty Principle for Hankel
    Transforms.” <i>Proceedings of the American Mathematical Society</i> 127, no.
    1 (1999): 183–194.'
  ieee: M. Rösler and M. Voit, “An uncertainty principle for Hankel transforms,” <i>Proceedings
    of the American Mathematical Society</i>, vol. 127, no. 1, pp. 183–194, 1999.
  mla: Rösler, Margit, and Michael Voit. “An Uncertainty Principle for Hankel Transforms.”
    <i>Proceedings of the American Mathematical Society</i>, vol. 127, no. 1, American
    Mathematical Society (AMS), 1999, pp. 183–194.
  short: M. Rösler, M. Voit, Proceedings of the American Mathematical Society 127
    (1999) 183–194.
date_created: 2023-01-30T11:20:49Z
date_updated: 2025-08-09T09:24:57Z
department:
- _id: '555'
extern: '1'
intvolume: '       127'
issue: '1'
language:
- iso: eng
page: 183–194
publication: Proceedings of the American Mathematical Society
publication_identifier:
  issn:
  - 0002-9939
  - 1088-6826
publication_status: published
publisher: American Mathematical Society (AMS)
status: public
title: An uncertainty principle for Hankel transforms
type: journal_article
user_id: '37390'
volume: 127
year: '1999'
...