---
_id: '34840'
abstract:
- lang: eng
  text: 'In this paper we obtain a complete list of imaginary n-quadratic fields with
    class groups of exponent 3 and 5 under ERH for every positive integer n where
    an n-quadratic field is a number field of degree 2ⁿ represented as the composite
    of n quadratic fields. '
author:
- first_name: Jürgen
  full_name: Klüners, Jürgen
  id: '21202'
  last_name: Klüners
- first_name: Toru
  full_name: Komatsu, Toru
  last_name: Komatsu
citation:
  ama: Klüners J, Komatsu T. Imaginary multiquadratic number fields with class group
    of exponent $3$ and $5$. <i>Mathematics of Computation</i>. 2021;90(329):1483-1497.
    doi:<a href="https://doi.org/10.1090/mcom/3609">10.1090/mcom/3609</a>
  apa: Klüners, J., &#38; Komatsu, T. (2021). Imaginary multiquadratic number fields
    with class group of exponent $3$ and $5$. <i>Mathematics of Computation</i>, <i>90</i>(329),
    1483–1497. <a href="https://doi.org/10.1090/mcom/3609">https://doi.org/10.1090/mcom/3609</a>
  bibtex: '@article{Klüners_Komatsu_2021, title={Imaginary multiquadratic number fields
    with class group of exponent $3$ and $5$}, volume={90}, DOI={<a href="https://doi.org/10.1090/mcom/3609">10.1090/mcom/3609</a>},
    number={329}, journal={Mathematics of Computation}, publisher={American Mathematical
    Society (AMS)}, author={Klüners, Jürgen and Komatsu, Toru}, year={2021}, pages={1483–1497}
    }'
  chicago: 'Klüners, Jürgen, and Toru Komatsu. “Imaginary Multiquadratic Number Fields
    with Class Group of Exponent $3$ and $5$.” <i>Mathematics of Computation</i> 90,
    no. 329 (2021): 1483–97. <a href="https://doi.org/10.1090/mcom/3609">https://doi.org/10.1090/mcom/3609</a>.'
  ieee: 'J. Klüners and T. Komatsu, “Imaginary multiquadratic number fields with class
    group of exponent $3$ and $5$,” <i>Mathematics of Computation</i>, vol. 90, no.
    329, pp. 1483–1497, 2021, doi: <a href="https://doi.org/10.1090/mcom/3609">10.1090/mcom/3609</a>.'
  mla: Klüners, Jürgen, and Toru Komatsu. “Imaginary Multiquadratic Number Fields
    with Class Group of Exponent $3$ and $5$.” <i>Mathematics of Computation</i>,
    vol. 90, no. 329, American Mathematical Society (AMS), 2021, pp. 1483–97, doi:<a
    href="https://doi.org/10.1090/mcom/3609">10.1090/mcom/3609</a>.
  short: J. Klüners, T. Komatsu, Mathematics of Computation 90 (2021) 1483–1497.
date_created: 2022-12-22T10:48:44Z
date_updated: 2023-03-06T08:57:45Z
department:
- _id: '102'
doi: 10.1090/mcom/3609
external_id:
  arxiv:
  - 2004.03308v2
intvolume: '        90'
issue: '329'
keyword:
- Applied Mathematics
- Computational Mathematics
- Algebra and Number Theory
language:
- iso: eng
page: 1483-1497
publication: Mathematics of Computation
publication_identifier:
  issn:
  - 0025-5718
  - 1088-6842
publication_status: published
publisher: American Mathematical Society (AMS)
status: public
title: Imaginary multiquadratic number fields with class group of exponent $3$ and
  $5$
type: journal_article
user_id: '93826'
volume: 90
year: '2021'
...
---
_id: '34912'
abstract:
- lang: eng
  text: 'Let E be an ordinary elliptic curve over a finite field and g be a positive
    integer. Under some technical assumptions, we give an algorithm to span the isomorphism
    classes of principally polarized abelian varieties in the isogeny class of E⁹
    . The varieties are first described as hermitian lattices over (not necessarily
    maximal) quadratic orders and then geometrically in terms of their algebraic theta
    null point. We also show how to algebraically compute Siegel modular forms of
    even weight given as polynomials in the theta constants by a careful choice of
    an affine lift of the theta null point. We then use these results to give an algebraic
    computation of Serre’s obstruction for principally polarized abelian threefolds
    isogenous to E³ and of the Igusa modular form in dimension 4. We illustrate our
    algorithms with examples of curves with many rational points over finite fields. '
author:
- first_name: Markus
  full_name: Kirschmer, Markus
  id: '82258'
  last_name: Kirschmer
- first_name: Fabien
  full_name: Narbonne, Fabien
  last_name: Narbonne
- first_name: Christophe
  full_name: Ritzenthaler, Christophe
  last_name: Ritzenthaler
- first_name: Damien
  full_name: Robert, Damien
  last_name: Robert
citation:
  ama: Kirschmer M, Narbonne F, Ritzenthaler C, Robert D. Spanning the isogeny class
    of a power of an elliptic curve. <i>Mathematics of Computation</i>. 2021;91(333):401-449.
    doi:<a href="https://doi.org/10.1090/mcom/3672">10.1090/mcom/3672</a>
  apa: Kirschmer, M., Narbonne, F., Ritzenthaler, C., &#38; Robert, D. (2021). Spanning
    the isogeny class of a power of an elliptic curve. <i>Mathematics of Computation</i>,
    <i>91</i>(333), 401–449. <a href="https://doi.org/10.1090/mcom/3672">https://doi.org/10.1090/mcom/3672</a>
  bibtex: '@article{Kirschmer_Narbonne_Ritzenthaler_Robert_2021, title={Spanning the
    isogeny class of a power of an elliptic curve}, volume={91}, DOI={<a href="https://doi.org/10.1090/mcom/3672">10.1090/mcom/3672</a>},
    number={333}, journal={Mathematics of Computation}, publisher={American Mathematical
    Society (AMS)}, author={Kirschmer, Markus and Narbonne, Fabien and Ritzenthaler,
    Christophe and Robert, Damien}, year={2021}, pages={401–449} }'
  chicago: 'Kirschmer, Markus, Fabien Narbonne, Christophe Ritzenthaler, and Damien
    Robert. “Spanning the Isogeny Class of a Power of an Elliptic Curve.” <i>Mathematics
    of Computation</i> 91, no. 333 (2021): 401–49. <a href="https://doi.org/10.1090/mcom/3672">https://doi.org/10.1090/mcom/3672</a>.'
  ieee: 'M. Kirschmer, F. Narbonne, C. Ritzenthaler, and D. Robert, “Spanning the
    isogeny class of a power of an elliptic curve,” <i>Mathematics of Computation</i>,
    vol. 91, no. 333, pp. 401–449, 2021, doi: <a href="https://doi.org/10.1090/mcom/3672">10.1090/mcom/3672</a>.'
  mla: Kirschmer, Markus, et al. “Spanning the Isogeny Class of a Power of an Elliptic
    Curve.” <i>Mathematics of Computation</i>, vol. 91, no. 333, American Mathematical
    Society (AMS), 2021, pp. 401–49, doi:<a href="https://doi.org/10.1090/mcom/3672">10.1090/mcom/3672</a>.
  short: M. Kirschmer, F. Narbonne, C. Ritzenthaler, D. Robert, Mathematics of Computation
    91 (2021) 401–449.
date_created: 2022-12-23T11:02:02Z
date_updated: 2023-04-04T07:52:43Z
department:
- _id: '102'
doi: 10.1090/mcom/3672
intvolume: '        91'
issue: '333'
keyword:
- Applied Mathematics
- Computational Mathematics
- Algebra and Number Theory
language:
- iso: eng
page: 401-449
publication: Mathematics of Computation
publication_identifier:
  issn:
  - 0025-5718
  - 1088-6842
publication_status: published
publisher: American Mathematical Society (AMS)
status: public
title: Spanning the isogeny class of a power of an elliptic curve
type: journal_article
user_id: '93826'
volume: 91
year: '2021'
...
---
_id: '45955'
author:
- first_name: Georgios
  full_name: Akrivis, Georgios
  last_name: Akrivis
- first_name: Michael
  full_name: Feischl, Michael
  last_name: Feischl
- first_name: Balázs
  full_name: Kovács, Balázs
  id: '100441'
  last_name: Kovács
  orcid: 0000-0001-9872-3474
- first_name: Christian
  full_name: Lubich, Christian
  last_name: Lubich
citation:
  ama: Akrivis G, Feischl M, Kovács B, Lubich C. Higher-order linearly implicit full
    discretization of the Landau–Lifshitz–Gilbert equation. <i>Mathematics of Computation</i>.
    2020;90(329):995-1038. doi:<a href="https://doi.org/10.1090/mcom/3597">10.1090/mcom/3597</a>
  apa: Akrivis, G., Feischl, M., Kovács, B., &#38; Lubich, C. (2020). Higher-order
    linearly implicit full discretization of the Landau–Lifshitz–Gilbert equation.
    <i>Mathematics of Computation</i>, <i>90</i>(329), 995–1038. <a href="https://doi.org/10.1090/mcom/3597">https://doi.org/10.1090/mcom/3597</a>
  bibtex: '@article{Akrivis_Feischl_Kovács_Lubich_2020, title={Higher-order linearly
    implicit full discretization of the Landau–Lifshitz–Gilbert equation}, volume={90},
    DOI={<a href="https://doi.org/10.1090/mcom/3597">10.1090/mcom/3597</a>}, number={329},
    journal={Mathematics of Computation}, publisher={American Mathematical Society
    (AMS)}, author={Akrivis, Georgios and Feischl, Michael and Kovács, Balázs and
    Lubich, Christian}, year={2020}, pages={995–1038} }'
  chicago: 'Akrivis, Georgios, Michael Feischl, Balázs Kovács, and Christian Lubich.
    “Higher-Order Linearly Implicit Full Discretization of the Landau–Lifshitz–Gilbert
    Equation.” <i>Mathematics of Computation</i> 90, no. 329 (2020): 995–1038. <a
    href="https://doi.org/10.1090/mcom/3597">https://doi.org/10.1090/mcom/3597</a>.'
  ieee: 'G. Akrivis, M. Feischl, B. Kovács, and C. Lubich, “Higher-order linearly
    implicit full discretization of the Landau–Lifshitz–Gilbert equation,” <i>Mathematics
    of Computation</i>, vol. 90, no. 329, pp. 995–1038, 2020, doi: <a href="https://doi.org/10.1090/mcom/3597">10.1090/mcom/3597</a>.'
  mla: Akrivis, Georgios, et al. “Higher-Order Linearly Implicit Full Discretization
    of the Landau–Lifshitz–Gilbert Equation.” <i>Mathematics of Computation</i>, vol.
    90, no. 329, American Mathematical Society (AMS), 2020, pp. 995–1038, doi:<a href="https://doi.org/10.1090/mcom/3597">10.1090/mcom/3597</a>.
  short: G. Akrivis, M. Feischl, B. Kovács, C. Lubich, Mathematics of Computation
    90 (2020) 995–1038.
date_created: 2023-07-10T11:42:57Z
date_updated: 2024-04-03T09:20:36Z
department:
- _id: '841'
doi: 10.1090/mcom/3597
intvolume: '        90'
issue: '329'
keyword:
- Applied Mathematics
- Computational Mathematics
- Algebra and Number Theory
language:
- iso: eng
page: 995-1038
publication: Mathematics of Computation
publication_identifier:
  issn:
  - 0025-5718
  - 1088-6842
publication_status: published
publisher: American Mathematical Society (AMS)
status: public
title: Higher-order linearly implicit full discretization of the Landau–Lifshitz–Gilbert
  equation
type: journal_article
user_id: '100441'
volume: 90
year: '2020'
...
---
_id: '42797'
abstract:
- lang: eng
  text: 'An efficient algorithm to compute automorphism groups and isometries of definite
    Fq[t]-lattices for odd q is presented. The algorithm requires several square root
    computations in Fq₂ but no enumeration of orbits having more than eight elements. '
author:
- first_name: Markus
  full_name: Kirschmer, Markus
  id: '82258'
  last_name: Kirschmer
citation:
  ama: Kirschmer M. A normal form for definite quadratic forms over $\mathbb{F}_{q}[t]$.
    <i>Mathematics of Computation</i>. 2012;81(279):1619-1634. doi:<a href="https://doi.org/10.1090/s0025-5718-2011-02570-6">10.1090/s0025-5718-2011-02570-6</a>
  apa: Kirschmer, M. (2012). A normal form for definite quadratic forms over $\mathbb{F}_{q}[t]$.
    <i>Mathematics of Computation</i>, <i>81</i>(279), 1619–1634. <a href="https://doi.org/10.1090/s0025-5718-2011-02570-6">https://doi.org/10.1090/s0025-5718-2011-02570-6</a>
  bibtex: '@article{Kirschmer_2012, title={A normal form for definite quadratic forms
    over $\mathbb{F}_{q}[t]$}, volume={81}, DOI={<a href="https://doi.org/10.1090/s0025-5718-2011-02570-6">10.1090/s0025-5718-2011-02570-6</a>},
    number={279}, journal={Mathematics of Computation}, publisher={American Mathematical
    Society (AMS)}, author={Kirschmer, Markus}, year={2012}, pages={1619–1634} }'
  chicago: 'Kirschmer, Markus. “A Normal Form for Definite Quadratic Forms over $\mathbb{F}_{q}[t]$.”
    <i>Mathematics of Computation</i> 81, no. 279 (2012): 1619–34. <a href="https://doi.org/10.1090/s0025-5718-2011-02570-6">https://doi.org/10.1090/s0025-5718-2011-02570-6</a>.'
  ieee: 'M. Kirschmer, “A normal form for definite quadratic forms over $\mathbb{F}_{q}[t]$,”
    <i>Mathematics of Computation</i>, vol. 81, no. 279, pp. 1619–1634, 2012, doi:
    <a href="https://doi.org/10.1090/s0025-5718-2011-02570-6">10.1090/s0025-5718-2011-02570-6</a>.'
  mla: Kirschmer, Markus. “A Normal Form for Definite Quadratic Forms over $\mathbb{F}_{q}[t]$.”
    <i>Mathematics of Computation</i>, vol. 81, no. 279, American Mathematical Society
    (AMS), 2012, pp. 1619–34, doi:<a href="https://doi.org/10.1090/s0025-5718-2011-02570-6">10.1090/s0025-5718-2011-02570-6</a>.
  short: M. Kirschmer, Mathematics of Computation 81 (2012) 1619–1634.
date_created: 2023-03-07T08:35:56Z
date_updated: 2023-04-04T09:22:22Z
department:
- _id: '102'
doi: 10.1090/s0025-5718-2011-02570-6
extern: '1'
intvolume: '        81'
issue: '279'
keyword:
- Applied Mathematics
- Computational Mathematics
- Algebra and Number Theory
language:
- iso: eng
page: 1619-1634
publication: Mathematics of Computation
publication_identifier:
  issn:
  - 0025-5718
  - 1088-6842
publication_status: published
publisher: American Mathematical Society (AMS)
status: public
title: A normal form for definite quadratic forms over $\mathbb{F}_{q}[t]$
type: journal_article
user_id: '93826'
volume: 81
year: '2012'
...
---
_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'
...