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International Algorithmic Number Theory Symposium

ANTS 2006: Algorithmic Number Theory pp 40–55Cite as

Cohen–Lenstra Heuristics of Quadratic Number Fields

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 4076))

Abstract

We establish a link between some heuristic asymptotic formulas (due to Cohen and Lenstra) concerning the moments of the p–part of the class groups of quadratic fields and formulas giving the frequency of the values of the p–rank of these class groups.

Furthermore we report on new results for 4–ranks of class groups of quadratic number fields.

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References

  1. Cohen, H., Lenstra, H.W.: Heuristics on class groups of number fields. In: Number theory, Noordwijkerhout 1983. Lecture Notes in Math., vol. 1068, pp. 33–62. Springer, Berlin (1984)

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Author information

Authors and Affiliations

  1. Mathématique, Bât. 425, Univ. Paris–Sud, Campus d’Orsay, F–91405 Cedex, ORSAY, France

    Étienne Fouvry

  2. Fachbereich Mathematik/Informatik, Universität Kassel, Heinrich-Plett-Str. 40, 34132, Kassel, Germany

    Jürgen Klüners

Authors
  1. Étienne Fouvry
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  2. Jürgen Klüners
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Editor information

Editors and Affiliations

  1. Technische Universität Berlin, Germany

    Florian Hess

  2. Institut für Mathematik, MA 8–1, Technische Universität Berlin, Straße des 17. Juni 136, 10623, Berlin, Germany

    Sebastian Pauli

  3. Institut für Mathematik, Technische Universität Berlin, Fakultät II, MA 8-1, Strasse des 17. Juni 136, 10623, Berlin, Germany

    Michael Pohst

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© 2006 Springer-Verlag Berlin Heidelberg

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Fouvry, É., Klüners, J. (2006). Cohen–Lenstra Heuristics of Quadratic Number Fields. In: Hess, F., Pauli, S., Pohst, M. (eds) Algorithmic Number Theory. ANTS 2006. Lecture Notes in Computer Science, vol 4076. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11792086_4

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  • DOI: https://doi.org/10.1007/11792086_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-36075-9

  • Online ISBN: 978-3-540-36076-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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