Publications Prof. Dr. Jürgen Klüners

Thesis:

  1. Diplomarbeit: Über die Berechnung von Teilkörpern algebraischer Zahlkörper, Technical University Berlin, 1995.
  2. Dissertation: Über die Berechnung von Automorphismen und Teilkörpern algebraischer Zahlkörper, Technical University Berlin, 1997.
  3. Habilitationsschrift: Über die Asymptotik von Zahlkörpern mit vorgegebener Galoisgruppe, University Kassel, 2005.
    My habilitation appeared as a book published by Shaker Verlag.
    Jürgen Klüners: Über die Asymptotik von Zahlkörpern mit vorgegebener Galoisgruppe
    (ISBN 3-8322-4003-9)

Papers:

  1. On Computing Subfields, (with M. Pohst), J.Symb.Comput., 24, 1997, 385-397.
  2. KANT V4, (with M. Daberkow, C. Fieker, M. Pohst, K. Roegner, M. Schoernig, K. Wildanger), J.Symb.Comput., 24, 1997, 267-283.
  3. On Computing Subfields - A Detailed Description of the Algorithm, Journal de Theorie des Nombres de Bordeaux, 10, 1998, 243-271.
  4. On Polynomial Decompositions, J.Symb.Comput., 27, 1999, 261-269.
  5. Computing Automorphisms of Abelian Number Fields, (with V. Acciaro), Math.Comput., 68, 1999, 1179-1186.
  6. Computing Local Artin Maps, and Solvability of Norm Equations, (with V. Acciaro), J.Symb.Comput., 30, 2000, 239-252.
  7. Galois Group Computation for Rational Polynomials, (with K. Geissler), J.Symb.Comput., 30, 2000, 653-674.
  8. Explicit Galois Realization of Transitive Groups of Degree up to 15, (with G. Malle), J.Symb.Comput., 30, 2000, 675-716.
  9. A Polynomial with Galois Group SL2(11), J.Symb.Comput., 30, 2000, 733-737.
  10. A Database for Field Extensions of the Rationals, (with G. Malle), LMS J. Comput. Math., 4, 2001, 182-196.
  11. Algorithms for Function Fields, Exp.Math., 11, 2002, 171-181.
  12. Minimal Discriminants for Fields with Small Frobenius Groups as Galois Groups, (with C. Fieker), J.Numb.Th., 99, 2003, 318-337.
  13. Counting Nilpotent Galois Extensions, (with G. Malle), J. reine angew. Math., 572, 2004, 1--26.
  14. A counterexample to Malle's Conjecture on the Asymptotics of Discriminants, C. R. Math. Acad. Sci. Paris, Ser. I 340, 2005, 411-414.
  15. Computing Residue Class Rings and Picard Groups of Orders, (with S. Pauli), J. Algebra, 292, 2005, 47-64.
  16. The Number of S4-Fields with Given Discriminant, Acta Arith., 122, 2006, 185--194.
  17. Cohen-Lenstra heuristics of quadratic number fields, (with E. Fouvry), in F. Hess, S. Pauli, and M. Pohst (Eds.), ANTS 2006, LNCS 4076, 2006, 40-55.
  18. Asymptotics of number fields and the Cohen-Lenstra heuristics, Journal de Théorie des Nombres de Bordeaux, 18, 2006, 607-615.
  19. On the 4-rank of class groups of quadratic number fields, (with E. Fouvry), Invent. math., 167, 2007, 455-513.
  20. Factoring Polynomials over Global fields, (with K. Belabas, M. van Hoeij, A. Steel),  Journal de Théorie des Nombres de Bordeaux, 21, 2009, 15-39.
  21. The van Hoeij Algorithm for Factoring Polynomials, in P. Q. Nguyen, B. Vallée (Eds.), The LLL Algorithm Survey and Applications, Information Security and Cryptography, Springer, 2010, 283-291.
  22. The parity of the period of the continued fraction of √d , (with E. Fouvry), Proceedings of the London Mathematical Society (3), 101, 2010, 337-391.
  23. On the Spiegelungssatz for the 4-Rank, (with E. Fouvry), Algebra and Number Theory, 4, 2010, 493–508
  24. On the negative Pell equation, (with E. Fouvry), Annals of Mathematics, 172, 2010, 2035-2104
  25. Weighted distribution of the 4-Rank of class groups and applications, (with E. Fouvry), in IMRN, 16, 2011, 3618-3656.
  26. Generating Subfields, (with M. van Hoeij, A. Novocin), in E. Schost, I.Z. Emiris (Eds.), ISSAC '11, ACM, 2011, 345-352.
  27. The distribution of number fields with wreath products as Galois groups, International Journal of Number Theory, 8, 2012, 845-858.
  28. Generating Subfields, (with M. von Hoeij, A. Novocin), J.Symb.Comput., 52, 2013, 17-34.
  29. Computation of Galois Groups of rational polynomials, (with C. Fieker), LMS Journal of Computation and Mathematics, 17, 2014, 141-158.
  30. Are number fields determined by Artin L-functions? (with F. Nicolae), J.Numb.Th., 167, 2016, 161-168.
  31. Computing subfields of number fields and applications to Galois group computations, (with A.-S. Elsenhans) J.Symb.Comput., 93, 2018, 1-20.
  32. Imaginary quadratic number fields with class groups of small exponent (with A.-S. Elsenhans, F. Nicolae), Acta Arith., 193, 2020, 217-233.
  33. The conductor density of local function fields (with R. Müller), J.Numb.Th., 212, 2020, 311-322.
  34. Imaginary multiquadratic number fields of exponent 3 and 5 (with Toru Komatsu), Math. Comp., 90, 2021, 1483-1497.
  35. ℓ-torsion bounds for the class group of number fields with an ℓ-group as Galois group (with Jiuya Wang), Proc. Amer. Math. Soc., 150, 2022, 2793–2805.
  36. The asymptotics of nilpotent Galois groups, Acta Arith., 204, 2022, 165-184.


Preprints:

  1. Chow groups of orders in number fields (with M. Kirschmer).
  2. Computing quadratic subfields of number fields (with A.-S. Elsenhans).

 

 

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