Papers - Computer Algebra and Number Theory

Chow groups of one-dimensional noetherian domains

M. Kirschmer, J. Klüners, Research in Number Theory 10 (2024).

DOI arXiv

Idélic Approach in Enumerating Heisenberg Extensions

J. Klüners, J. Wang, La Matematica (2023).

DOI

ℓ-torsion bounds for the class group of number fields with an ℓ-group as Galois group

J. Klüners, J. Wang, Proceedings of the American Mathematical Society 150 (2022) 2793–2805.

DOI arXiv

The asymptotics of nilpotent Galois groups

J. Klüners, Acta Arithmetica 204 (2022) 165–184.

DOI arXiv

Imaginary multiquadratic number fields with class group of exponent $3$ and $5$

J. Klüners, T. Komatsu, Mathematics of Computation 90 (2021) 1483–1497.

DOI arXiv

Imaginary quadratic number fields with class groups of small exponent

A.-S. Elsenhans, J. Klüners, F. Nicolae, Acta Arithmetica 193 (2020) 217–233.

DOI arXiv

The conductor density of local function fields with abelian Galois group

J. Klüners, R. Müller, Journal of Number Theory 212 (2020) 311–322.

DOI arXiv

Computing subfields of number fields and applications to Galois group computations

A.-S. Elsenhans, J. Klüners, Journal of Symbolic Computation 93 (2018) 1–20.

DOI arXiv

Are number fields determined by Artin L-functions?

J. Klüners, F. Nicolae, Journal of Number Theory 167 (2016) 161–168.

DOI arXiv

Computation of Galois groups of rational polynomials

C. Fieker, J. Klüners, LMS Journal of Computation and Mathematics 17 (2014) 141–158.

DOI arXiv

The Distribution of Number Fields with Wreath Products as Galois Groups

J. Klüners, International Journal of Number Theory 08 (2012) 845–858.

DOI arXiv

Weighted Distribution of the 4-rank of Class Groups and Applications

É. Fouvry, J. Klüners, International Mathematics Research Notices 2011 (2011) 3618–3656.

DOI

Generating subfields

M. van Hoeij, J. Klüners, A. Novocin, Journal of Symbolic Computation 52 (2011) 17–34.

DOI

On the negative Pell equation

É. Fouvry, J. Klüners, Annals of Mathematics 172 (2010) 2035–2104.

DOI

The parity of the period of the continued fraction of d

É. Fouvry, J. Klüners, Proceedings of the London Mathematical Society 101 (2010) 337–391.

DOI https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=fc7ab412993fd2bf0069de42fbef1ecc69137755

On the Spiegelungssatz for the 4-rank

É. Fouvry, J. Klüners, Algebra & Number Theory 4 (2010) 493–508.

DOI

Factoring polynomials over global fields

K. Belabas, M. van Hoeij, J. Klüners, A. Steel, Journal de Théorie Des Nombres de Bordeaux 21 (2009) 15–39.

DOI arXiv

The van Hoeij Algorithm for Factoring Polynomials

J. Klüners, in: The LLL Algorithm, Springer Berlin Heidelberg, Berlin, Heidelberg, 2009.

DOI https://www.researchgate.net/profile/Juergen-Klueners/publication/226764840_The_van_Hoeij_Algorithm_for_Factoring_Polynomials/links/00463532f2216a64ae000000/The-van-Hoeij-Algorithm-for-Factoring-Polynomials.pdf?origin=publication_detail

Counting nilpotent Galois extensions

J. Klüners, G. Malle, Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal) 2004 (2006) 1–26.

DOI arXiv

Asymptotics of number fields and the Cohen–Lenstra heuristics

J. Klüners, Journal de Théorie Des Nombres de Bordeaux 18 (2006) 607–615.

DOI arXiv

On the 4-rank of class groups of quadratic number fields

É. Fouvry, J. Klüners, Inventiones Mathematicae 167 (2006) 455–513.

DOI https://math.uni-paderborn.de/fileadmin/mathematik/AG-Computeralgebra/Publications-klueners/ranks.pdf

Cohen–Lenstra Heuristics of Quadratic Number Fields

É. Fouvry, J. Klüners, in: Lecture Notes in Computer Science, Springer Berlin Heidelberg, Berlin, Heidelberg, 2006.

DOI https://www.researchgate.net/profile/Juergen-Klueners/publication/221451567_Cohen-Lenstra_Heuristics_of_Quadratic_Number_Fields/links/0a85e53298eaed8777000000/Cohen-Lenstra-Heuristics-of-Quadratic-Number-Fields.pdf?origin=publication_detail

The number of S₄-fields with given discriminant

J. Klüners, Acta Arithmetica 122 (2006) 185–194.

DOI arXiv

A counter example to Malle's conjecture on the asymptotics of discriminants

J. Klüners, Comptes Rendus Mathematique 340 (2005) 411–414.

DOI arXiv

Computing residue class rings and Picard groups of orders

J. Klüners, S. Pauli, Journal of Algebra 292 (2005) 47–64.

DOI

Minimal discriminants for fields with small Frobenius groups as Galois groups

C. Fieker, J. Klüners, Journal of Number Theory 99 (2003) 318–337.

DOI

Algorithms for function fields

J. Klüners, Experiment. Math. 11 (2002) 171–181.

https://projecteuclid.org/journals/experimental-mathematics/volume-11/issue-2/Algorithms-for-function-fields/em/1062621213.full

A Database for Field Extensions of the Rationals

J. Klüners, G. Malle, LMS Journal of Computation and Mathematics 4 (2001) 182–196.

DOI arXiv

Galois Group Computation for Rational Polynomials

K. Geissler, J. Klüners, Journal of Symbolic Computation 30 (2000) 653–674.

DOI

Computing Local Artin Maps, and Solvability of Norm Equations

V. Acciaro, J. Klüners, Journal of Symbolic Computation 30 (2000) 239–252.

DOI

Explicit Galois Realization of Transitive Groups of Degree up to 15

J. Klüners, G. Malle, Journal of Symbolic Computation 30 (2000) 675–716.

DOI

A Polynomial with Galois GroupSL2(11)

J. Klüners, Journal of Symbolic Computation 30 (2000) 733–737.

DOI

On Polynomial Decompositions

J. Klüners, Journal of Symbolic Computation 27 (1999) 261–269.

DOI

Computing Automorphisms of Abelian Number Fields

J. Klüners, V. Acciaro, Mathematics of Computation 68 (1999) 1179–1186.

https://www.ams.org/journals/mcom/1999-68-227/S0025-5718-99-01084-4/S0025-5718-99-01084-4.pdf

On computing subfields. A detailed description of the algorithm

J. Klüners, Journal de Theorie Des Nombres de Bordeaux 10 (1998) 243–271.

DOI http://www.numdam.org/item/JTNB_1998__10_2_243_0/

KANT V4

M. DABERKOW, C. FIEKER, J. Klüners, M. POHST, K. ROEGNER, M. SCHÖRNIG, K. WILDANGER, Journal of Symbolic Computation 24 (1997) 267–283.

DOI

On Computing Subfields

J. Klüners, M. Pohst, Journal of Symbolic Computation 24 (1997) 385–397.

DOI